Sasi Math (Revised for 1024)

Scroll:Probability >> Multiple choice question >> mcq (4520)

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.

There are 9 defective items in a sample of 17 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 817 ' title="

\frac{8}{17}

"/>

\frac{8}{17}

2) 917 ' title="

\frac{9}{17}

"/>

\frac{9}{17}

3) 179 ' title="

\frac{17}{9}

"/>

\frac{17}{9}

4) 817 ' title="

\frac{8}{17}

"/>

\frac{8}{17}

( )

Let A and B be any two events and S be the corresponding sample space, Then P(A∩B) ____

(A) p(B) - P(A∩B) (B) P(A∩B) - P(B)

1) A
2) B
3) C
4) D

( )

The probability that a student will score centum in mathematics is $\frac{4}{9}$ . The probability that be will not score centum is _____

1) 59 ' title="

\frac{5}{9}

"/>

\frac{5}{9}

2) 39 ' title="

\frac{3}{9}

"/>

\frac{3}{9}

3) 69 ' title="

\frac{6}{9}

"/>

\frac{6}{9}

4) 59 ' title="

\frac{5}{9}

"/>

\frac{5}{9}

( )

If A and B are two events such that P(A) = 0.85, P(B) = 0.95 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 1.45
2) 0.95
3) 2.45
4) 1.95

( )

The probabilities of three mutually exclusive A,B and C are given by $\frac{1}{3}$ , $\frac{1}{4}$ and $\frac{5}{12.}$ then P(A U B U C) is _______.

(A) $\frac{19}{12}$ (B) $\frac{11}{12}$ (C) $\frac{7}{12}$ (D) 1

1) B
2) C
3) D
4) A

( )

If S is the sample space of a random experiment, then P(S) ______

1) 0
2) 18' title="

\frac{1}{8}

"/>

\frac{1}{8}

3) 1
4) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

( )

If Ø is an impossible event, then P(Ø) = ______

1) 14' title="

\frac{1}{4}

"/>

\frac{1}{4}

2) 1
3) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

4) 0

( )

If P is the probability of an event A, then P satisfies ______

(A) 0 < P < 1 (B) 0 < P < 1

1) D
2) A
3) B
4) C

( )

There are 5 defective items in a sample of 20 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 205 ' title="

\frac{20}{5}

"/>

\frac{20}{5}

2) 15 ' title="

\frac{1}{5}

"/>

\frac{1}{5}

3) 34 ' title="

\frac{3}{4}

"/>

\frac{3}{4}

4) 520 ' title="

\frac{5}{20}

"/>

\frac{5}{20}

( )

10)

Let A and B be any two events and S be the corresponding sample space, Then P(A∩B) ____

(A) p(B) - P(A∩B) (B) P(A∩B) - P(B)

1) A
2) B
3) C
4) D

( )

There are 9 defective items in a sample of 17 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 179 ' title="

\frac{17}{9}

"/>

\frac{17}{9}

2) 817 ' title="

\frac{8}{17}

"/>

\frac{8}{17}

3) 817 ' title="

\frac{8}{17}

"/>

\frac{8}{17}

4) 917 ' title="

\frac{9}{17}

"/>

\frac{9}{17}

Answer: 3

SOLUTION 1 :

Given:

n(S) = 17

Number of non-defective item = 17 - 9

n(A) = 8.

P(A) = $\frac{n(A)}{n(S)}$ = $\frac{8}{17}$ = $\frac{8}{17}$

Ans = $\frac{8}{17}$ .

Let A and B be any two events and S be the corresponding sample space, Then P(A∩B) ____

(A) p(B) - P(A∩B) (B) P(A∩B) - P(B)

1) C
2) D
3) B
4) A

Answer: 4

SOLUTION 1 :

P(¯A∩B) = p(B) - P(A∩B)

Ans = (A) = P(B) - P(A∩B)

The probability that a student will score centum in mathematics is $\frac{2}{7}$ . The probability that be will not score centum is _____

1) 57 ' title="

\frac{5}{7}

"/>

\frac{5}{7}

2) 17 ' title="

\frac{1}{7}

"/>

\frac{1}{7}

3) 47 ' title="

\frac{4}{7}

"/>

\frac{4}{7}

4) 37 ' title="

\frac{3}{7}

"/>

\frac{3}{7}

Answer: 1

SOLUTION 1 :

P(M) = $\frac{2}{7}$

w.k.t P(M) + P(M¯) = 1

$\frac{2}{7}$ + P(M¯) = 1

P(M¯) = 1 - $\frac{2}{7}$

P(M¯) = 7-2 / 7

= $\frac{5}{7}$

Ans = $\frac{5}{7}$

If A and B are two events such that P(A) = 0.85, P(B) = 0.95 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 1.95
2) 0.95
3) 1.45
4) 2.45

Answer: 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 awa

PA) = 0.85

P(B) = 0.95

P(A∩B) = 0.35

P(A∪B)= P(A) + P(B) - P(A∩B)

= 0.85 + 0.95 - 0.35

= 0.85 + 0.6

= 1.45

The probabilities of three mutually exclusive A,B and C are given by $\frac{1}{3}$ , $\frac{1}{4}$ and $\frac{5}{12.}$ then P(A U B U C) is _______.

(A) $\frac{19}{12}$ (B) $\frac{11}{12}$ (C) $\frac{7}{12}$ (D) 1

1) A
2) B
3) C
4) D

Answer: 4

SOLUTION 1 :

A, B and C are mutually exclusive events.

P(AUBUC) = P(A) + P(B) + P(C)

= $\frac{1}{3}$ + $\frac{1}{4}$ + $\frac{5}{12}$ = 4+3+5 /12

= $\frac{12}{12}$ = 1

If S is the sample space of a random experiment, then P(S) ______

1) 1
2) 0
3) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

4) 18' title="

\frac{1}{8}

"/>

\frac{1}{8}

Answer: 1

SOLUTION 1 :

P(S) = $\frac{n(S)}{n(S)}$ = 1

Ans= 1

If Ø is an impossible event, then P(Ø) = ______

1) 0
2) 1
3) 14' title="

\frac{1}{4}

"/>

\frac{1}{4}

4) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

Answer: 1

SOLUTION 1 :

Probability of an impossible event.

P(Ø) = 0.

If P is the probability of an event A, then P satisfies ______

(A) 0 < P < 1 (B) 0 < P < 1

1) D
2) B
3) C
4) A

Answer: 1

SOLUTION 1 :

If P is the probability of an event A then P satisfies, 0 < P < 1.

Ans (D) = 0 < P < 1

There are 5 defective items in a sample of 20 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 205 ' title="

\frac{20}{5}

"/>

\frac{20}{5}

2) 520 ' title="

\frac{5}{20}

"/>

\frac{5}{20}

3) 15 ' title="

\frac{1}{5}

"/>

\frac{1}{5}

4) 34 ' title="

\frac{3}{4}

"/>

\frac{3}{4}

Answer: 4

SOLUTION 1 :

Given:

n(S) = 20

Number of non-defective item = 20 - 5

n(A) = 15.

P(A) = $\frac{n(A)}{n(S)}$ = 1 $\frac{5}{20}$ = $\frac{3}{4}$

Ans = $\frac{3}{4}$ .

10)

Let A and B be any two events and S be the corresponding sample space, Then P(A∩B) ____

(A) p(B) - P(A∩B) (B) P(A∩B) - P(B)

1) C
2) A
3) D
4) B

Answer: 2

SOLUTION 1 :

P(¯A∩B) = p(B) - P(A∩B)

Ans = (A) = P(B) - P(A∩B)