Scroll:Probability >> Addition theorem on probability >> ps (4499)


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)  

 A bag contains 40 bolts and 130 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




2)  

 A bag contains 30 bolts and 150 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




3)  

 A bag contains 40 bolts and 100 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




4)  

 A bag contains 40 bolts and 150 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




5)  

 A bag contains 50 bolts and 130 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




6)  

 A bag contains 50 bolts and 150 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




7)  

 A bag contains 50 bolts and 110 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




8)  

 A bag contains 50 bolts and 100 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




9)  

 A bag contains 40 bolts and 190 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




10)  

 A bag contains 50 bolts and 190 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.


Answer:_______________




 

1)  

 A bag contains 40 bolts and 130 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 2134


SOLUTION 1 :

A bag contains 40 bolts and 130 nuts.

n(S) = 170.

If half of the bolts ( 40 bolts ) and half of the nuts ( 65 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (40) = 20.

No.of rusted nuts = 12 (130) = 65.

n(A) = 20 + 65 = 85 .

P(A) = n(A) / n(S) = 85170.

Let B be the event of an item is chosen which is bolt.

n(B) = 40

P(B) = n(B) / n(S) = 40170.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 20

P(A∩B) = n(AB) / n(S) = 20170 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   85170  + 40170  - 20170 = 105 / 170

             = 105170  

             =     2134



2)  

 A bag contains 30 bolts and 150 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 712


SOLUTION 1 :

A bag contains 30 bolts and 150 nuts.

n(S) = 180.

If half of the bolts ( 30 bolts ) and half of the nuts ( 75 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (30) = 15.

No.of rusted nuts = 12 (150) = 75.

n(A) = 15 + 75 = 90 .

P(A) = n(A) / n(S) = 90180.

Let B be the event of an item is chosen which is bolt.

n(B) = 30

P(B) = n(B) / n(S) = 30180.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 15

P(A∩B) = n(AB) / n(S) = 15180 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   90180  + 30180  - 15180 = 105 / 180

             = 105180  

             =     712



3)  

 A bag contains 40 bolts and 100 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 914


SOLUTION 1 :

A bag contains 40 bolts and 100 nuts.

n(S) = 140.

If half of the bolts ( 40 bolts ) and half of the nuts ( 50 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (40) = 20.

No.of rusted nuts = 12 (100) = 50.

n(A) = 20 + 50 = 70 .

P(A) = n(A) / n(S) = 70140.

Let B be the event of an item is chosen which is bolt.

n(B) = 40

P(B) = n(B) / n(S) = 40140.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 20

P(A∩B) = n(AB) / n(S) = 20140 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   70140  + 40140  - 20140 = 90 / 140

             = 90140  

             =     914



4)  

 A bag contains 40 bolts and 150 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 2338


SOLUTION 1 :

A bag contains 40 bolts and 150 nuts.

n(S) = 190.

If half of the bolts ( 40 bolts ) and half of the nuts ( 75 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (40) = 20.

No.of rusted nuts = 12 (150) = 75.

n(A) = 20 + 75 = 95 .

P(A) = n(A) / n(S) = 95190.

Let B be the event of an item is chosen which is bolt.

n(B) = 40

P(B) = n(B) / n(S) = 40190.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 20

P(A∩B) = n(AB) / n(S) = 20190 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   95190  + 40190  - 20190 = 115 / 190

             = 115190  

             =     2338



5)  

 A bag contains 50 bolts and 130 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 2336


SOLUTION 1 :

A bag contains 50 bolts and 130 nuts.

n(S) = 180.

If half of the bolts ( 50 bolts ) and half of the nuts ( 65 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (50) = 25.

No.of rusted nuts = 12 (130) = 65.

n(A) = 25 + 65 = 90 .

P(A) = n(A) / n(S) = 90180.

Let B be the event of an item is chosen which is bolt.

n(B) = 50

P(B) = n(B) / n(S) = 50180.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 25

P(A∩B) = n(AB) / n(S) = 25180 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   90180  + 50180  - 25180 = 115 / 180

             = 115180  

             =     2336



6)  

 A bag contains 50 bolts and 150 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 58


SOLUTION 1 :

A bag contains 50 bolts and 150 nuts.

n(S) = 200.

If half of the bolts ( 50 bolts ) and half of the nuts ( 75 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (50) = 25.

No.of rusted nuts = 12 (150) = 75.

n(A) = 25 + 75 = 100 .

P(A) = n(A) / n(S) = 100200.

Let B be the event of an item is chosen which is bolt.

n(B) = 50

P(B) = n(B) / n(S) = 50200.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 25

P(A∩B) = n(AB) / n(S) = 25200 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   100200  + 50200  - 25200 = 125 / 200

             = 1 25200  

             =     58



7)  

 A bag contains 50 bolts and 110 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 2132


SOLUTION 1 :

A bag contains 50 bolts and 110 nuts.

n(S) = 160.

If half of the bolts ( 50 bolts ) and half of the nuts ( 55 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (50) = 25.

No.of rusted nuts = 12 (110) = 55.

n(A) = 25 + 55 = 80 .

P(A) = n(A) / n(S) = 80160.

Let B be the event of an item is chosen which is bolt.

n(B) = 50

P(B) = n(B) / n(S) = 50160.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 25

P(A∩B) = n(AB) / n(S) = 25160 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   80160  + 50160  - 25160 = 105 / 160

             = 105160  

             =     2132



8)  

 A bag contains 50 bolts and 100 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 23


SOLUTION 1 :

A bag contains 50 bolts and 100 nuts.

n(S) = 150.

If half of the bolts ( 50 bolts ) and half of the nuts ( 50 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (50) = 25.

No.of rusted nuts = 12 (100) = 50.

n(A) = 25 + 50 = 75 .

P(A) = n(A) / n(S) = 75150.

Let B be the event of an item is chosen which is bolt.

n(B) = 50

P(B) = n(B) / n(S) = 50150.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 25

P(A∩B) = n(AB) / n(S) = 25150 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   75150  + 50150  - 25150 = 100 / 150

             = 100150  

             =     23



9)  

 A bag contains 40 bolts and 190 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 2746


SOLUTION 1 :

A bag contains 40 bolts and 190 nuts.

n(S) = 230.

If half of the bolts ( 40 bolts ) and half of the nuts ( 95 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (40) = 20.

No.of rusted nuts = 12 (190) = 95.

n(A) = 20 + 95 = 115 .

P(A) = n(A) / n(S) = 115230.

Let B be the event of an item is chosen which is bolt.

n(B) = 40

P(B) = n(B) / n(S) = 40230.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 20

P(A∩B) = n(AB) / n(S) = 20230 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   115230  + 40230  - 20230 = 135 / 230

             = 135230  

             =     2746



10)  

 A bag contains 50 bolts and 190 nuts . Half of the bolts and half of the nuts are ruted. If an item is chosen at random, find the probability that it is rusted or that it is a bolt.

Answer: 2948


SOLUTION 1 :

A bag contains 50 bolts and 190 nuts.

n(S) = 240.

If half of the bolts ( 50 bolts ) and half of the nuts ( 95 nuts ) are rusted.

Let A be the event of an item is chosen which is rusted item.

No.of ruted bolts = 12 (50) = 25.

No.of rusted nuts = 12 (190) = 95.

n(A) = 25 + 95 = 120 .

P(A) = n(A) / n(S) = 120240.

Let B be the event of an item is chosen which is bolt.

n(B) = 50

P(B) = n(B) / n(S) = 50240.

Let A∩B be the event of an item which is rusted bolt.

n(A∩B) = 25

P(A∩B) = n(AB) / n(S) = 25240 .

Sinces A and B are not mutully excusive,

P(A∪B) = P(A) + P(B) - P(A∩B) .

             =   120240  + 50240  - 25240 = 145 / 240

             = 145240  

             =     2948