Written Instructions:
For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..
For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.
Leave your answers in the simplest form or correct to two decimal places.
| 1) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.75 and the probability that it will get both the awards is 0.35. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 2) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.95 and the probability that it will get both the awards is 0.35. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 3) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.85 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 4) The probability that a new car will get an award for its design is 0.95 the probabilty that it will get an award for efficient use of fuel is 0.75 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 5) The probability that a new car will get an award for its design is 0.75 the probabilty that it will get an award for efficient use of fuel is 0.95 and the probability that it will get both the awards is 0.35. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 6) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.65 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 7) The probability that a new car will get an award for its design is 0.95 the probabilty that it will get an award for efficient use of fuel is 0.65 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 8) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.85 and the probability that it will get both the awards is 0.25. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 9) The probability that a new car will get an award for its design is 0.95 the probabilty that it will get an award for efficient use of fuel is 0.55 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 10) The probability that a new car will get an award for its design is 0.75 the probabilty that it will get an award for efficient use of fuel is 0.85 and the probability that it will get both the awards is 0.35. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... (ii) .. Answer:_______________ |
| 1) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.75 and the probability that it will get both the awards is 0.35. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 0.95 (ii) .. Answer: 0.6 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.55 P(B) = 0.75 P(A∩B) = 0.35 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.55 + 0.75 - 0.35 = 0.55 + 0.4 = 0.95 Car will get at least one of the awards = 0.95. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.55 - 0.35 ] + [ 0.75 - 0.35 ] = 0.2 + 0.4 = 0.6 Car will get only one of the awards = 0.6.
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| 2) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.95 and the probability that it will get both the awards is 0.35. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 1.15 (ii) .. Answer: 0.8 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.55 P(B) = 0.95 P(A∩B) = 0.35 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.55 + 0.95 - 0.35 = 0.55 + 0.6 = 1.15 Car will get at least one of the awards = 1.15. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.55 - 0.35 ] + [ 0.95 - 0.35 ] = 0.2 + 0.6 = 0.8 Car will get only one of the awards = 0.8.
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| 3) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.85 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 1.25 (ii) .. Answer: 1.1 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.55 P(B) = 0.85 P(A∩B) = 0.15 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.55 + 0.85 - 0.15 = 0.55 + 0.7 = 1.25 Car will get at least one of the awards = 1.25. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.55 - 0.15 ] + [ 0.85 - 0.15 ] = 0.4 + 0.7 = 1.1 Car will get only one of the awards = 1.1.
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| 4) The probability that a new car will get an award for its design is 0.95 the probabilty that it will get an award for efficient use of fuel is 0.75 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 1.55 (ii) .. Answer: 1.4 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.95 P(B) = 0.75 P(A∩B) = 0.15 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.95 + 0.75 - 0.15 = 0.95 + 0.6 = 1.55 Car will get at least one of the awards = 1.55. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.95 - 0.15 ] + [ 0.75 - 0.15 ] = 0.8 + 0.6 = 1.4 Car will get only one of the awards = 1.4.
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| 5) The probability that a new car will get an award for its design is 0.75 the probabilty that it will get an award for efficient use of fuel is 0.95 and the probability that it will get both the awards is 0.35. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 1.35 (ii) .. Answer: 1 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.75 P(B) = 0.95 P(A∩B) = 0.35 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.75 + 0.95 - 0.35 = 0.75 + 0.6 = 1.35 Car will get at least one of the awards = 1.35. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.75 - 0.35 ] + [ 0.95 - 0.35 ] = 0.4 + 0.6 = 1 Car will get only one of the awards = 1.
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| 6) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.65 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 1.05 (ii) .. Answer: 0.9 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.55 P(B) = 0.65 P(A∩B) = 0.15 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.55 + 0.65 - 0.15 = 0.55 + 0.5 = 1.05 Car will get at least one of the awards = 1.05. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.55 - 0.15 ] + [ 0.65 - 0.15 ] = 0.4 + 0.5 = 0.9 Car will get only one of the awards = 0.9.
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| 7) The probability that a new car will get an award for its design is 0.95 the probabilty that it will get an award for efficient use of fuel is 0.65 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 1.45 (ii) .. Answer: 1.3 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.95 P(B) = 0.65 P(A∩B) = 0.15 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.95 + 0.65 - 0.15 = 0.95 + 0.5 = 1.45 Car will get at least one of the awards = 1.45. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.95 - 0.15 ] + [ 0.65 - 0.15 ] = 0.8 + 0.5 = 1.3 Car will get only one of the awards = 1.3.
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| 8) The probability that a new car will get an award for its design is 0.55 the probabilty that it will get an award for efficient use of fuel is 0.85 and the probability that it will get both the awards is 0.25. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 1.15 (ii) .. Answer: 0.9 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.55 P(B) = 0.85 P(A∩B) = 0.25 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.55 + 0.85 - 0.25 = 0.55 + 0.6 = 1.15 Car will get at least one of the awards = 1.15. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.55 - 0.25 ] + [ 0.85 - 0.25 ] = 0.3 + 0.6 = 0.9 Car will get only one of the awards = 0.9.
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| 9) The probability that a new car will get an award for its design is 0.95 the probabilty that it will get an award for efficient use of fuel is 0.55 and the probability that it will get both the awards is 0.15. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 1.35 (ii) .. Answer: 1.2 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.95 P(B) = 0.55 P(A∩B) = 0.15 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.95 + 0.55 - 0.15 = 0.95 + 0.4 = 1.35 Car will get at least one of the awards = 1.35. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.95 - 0.15 ] + [ 0.55 - 0.15 ] = 0.8 + 0.4 = 1.2 Car will get only one of the awards = 1.2.
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| 10) The probability that a new car will get an award for its design is 0.75 the probabilty that it will get an award for efficient use of fuel is 0.85 and the probability that it will get both the awards is 0.35. Find the probability that (i) ... it will get atleast one of the two awards. (ii) ... it will get only one of the awards. (i) ... Answer: 1.25 (ii) .. Answer: 0.9 SOLUTION 1 : Let A be the event of getting an award for the design of car and B be the event of getting an award for efficient use of fuel. PA) = 0.75 P(B) = 0.85 P(A∩B) = 0.35 (i) ... P( Car will get at least one of the awards ) = P(A∪B) = P(A) + P(B) - P(A∩B) = 0.75 + 0.85 - 0.35 = 0.75 + 0.5 = 1.25 Car will get at least one of the awards = 1.25. (ii) .. P( Car will get only one of the awards ) = P ( Only A or only B ). = P(A∩¯B) + P(¯A∩B) = [ P(A) - P(A∩B) ] + [ P(B) - P(A∩B) ] = [ 0.75 - 0.35 ] + [ 0.85 - 0.35 ] = 0.4 + 0.5 = 0.9 Car will get only one of the awards = 0.9.
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