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.

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

1) 1
2) 0
3) 18' title="

\frac{1}{8}

"/>

\frac{1}{8}

4) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

( )

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) A
4) D

( )

There are 8 defective items in a sample of 21 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 13 ' title="

\frac{1}{3}

"/>

\frac{1}{3}

2) 821 ' title="

\frac{8}{21}

"/>

\frac{8}{21}

3) 1321 ' title="

\frac{13}{21}

"/>

\frac{13}{21}

4) 218 ' title="

\frac{21}{8}

"/>

\frac{21}{8}

( )

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

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

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

( )

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}

( )

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

1) 14' title="

\frac{1}{4}

"/>

\frac{1}{4}

2) 0
3) 1
4) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

( )

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) B
4) D

( )

If A and B are two events such that P(A) = 0.85, P(B) = 0.75 and P(A∩B) = 0.25, then P(A∪B) = _______

1) 1.35
2) 1.85
3) 2.35
4) 0.85

( )

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

1) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

2) 1
3) 18' title="

\frac{1}{8}

"/>

\frac{1}{8}

4) 0

( )

10)

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) C
2) B
3) A
4) D

( )

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) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

4) 1

Answer: 4

SOLUTION 1 :

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

Ans= 1

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) D
2) B
3) A
4) C

Answer: 1

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

There are 8 defective items in a sample of 21 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 821 ' title="

\frac{8}{21}

"/>

\frac{8}{21}

2) 218 ' title="

\frac{21}{8}

"/>

\frac{21}{8}

3) 13 ' title="

\frac{1}{3}

"/>

\frac{1}{3}

4) 1321 ' title="

\frac{13}{21}

"/>

\frac{13}{21}

Answer: 4

SOLUTION 1 :

Given:

n(S) = 21

Number of non-defective item = 21 - 8

n(A) = 13.

P(A) = $\frac{n(A)}{n(S)}$ = $\frac{13}{21}$ = $\frac{13}{21}$

Ans = $\frac{13}{21}$ .

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

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

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

Answer: 4

SOLUTION 1 :

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

Ans (D) = 0 < P < 1

The probability that a student will score centum in mathematics is $\frac{3}{9}$ . The probability that be will not score centum is _____

1) 59 ' title="

\frac{5}{9}

"/>

\frac{5}{9}

2) 69 ' title="

\frac{6}{9}

"/>

\frac{6}{9}

3) 29 ' title="

\frac{2}{9}

"/>

\frac{2}{9}

4) 49 ' title="

\frac{4}{9}

"/>

\frac{4}{9}

Answer: 2

SOLUTION 1 :

P(M) = $\frac{3}{9}$

w.k.t P(M) + P(M¯) = 1

$\frac{3}{9}$ + P(M¯) = 1

P(M¯) = 1 - $\frac{3}{9}$

P(M¯) = 9-3 / 9

= $\frac{6}{9}$

Ans = $\frac{6}{9}$

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

1) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

2) 1
3) 0
4) 14' title="

\frac{1}{4}

"/>

\frac{1}{4}

Answer: 3

SOLUTION 1 :

Probability of an impossible event.

P(Ø) = 0.

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)

If A and B are two events such that P(A) = 0.85, P(B) = 0.75 and P(A∩B) = 0.25, then P(A∪B) = _______

1) 0.85
2) 2.35
3) 1.35
4) 1.85

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) = 0.75

P(A∩B) = 0.25

P(A∪B)= P(A) + P(B) - P(A∩B)

= 0.85 + 0.75 - 0.25

= 0.85 + 0.5

= 1.35

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

1) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

2) 1
3) 0
4) 18' title="

\frac{1}{8}

"/>

\frac{1}{8}

Answer: 2

SOLUTION 1 :

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

Ans= 1

10)

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) C
2) B
3) A
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