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.

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

( )

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

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

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

( )

If A and B are two events such that P(A) = 0.65, P(B) = 0.55 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 0.85
2) 1.85
3) 1.35
4) 0.35

( )

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

1) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

2) 14' title="

\frac{1}{4}

"/>

\frac{1}{4}

3) 0
4) 1

( )

The probability that a student will score centum in mathematics is $\frac{2}{9}$ . The probability that be will not score centum is _____

1) 19 ' title="

\frac{1}{9}

"/>

\frac{1}{9}

2) 79 ' title="

\frac{7}{9}

"/>

\frac{7}{9}

3) 39 ' title="

\frac{3}{9}

"/>

\frac{3}{9}

4) 49 ' title="

\frac{4}{9}

"/>

\frac{4}{9}

( )

There are 7 defective items in a sample of 12 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 127 ' title="

\frac{12}{7}

"/>

\frac{12}{7}

2) 12 ' title="

\frac{1}{2}

"/>

\frac{1}{2}

3) 712 ' title="

\frac{7}{12}

"/>

\frac{7}{12}

4) 512 ' title="

\frac{5}{12}

"/>

\frac{5}{12}

( )

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

1) 0
2) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

3) 18' title="

\frac{1}{8}

"/>

\frac{1}{8}

4) 1

( )

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) B
2) C
3) A
4) D

( )

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) D
3) A
4) B

( )

10)

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

( )

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) A
3) B
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 P is the probability of an event A, then P satisfies ______

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

1) C
2) A
3) B
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

If A and B are two events such that P(A) = 0.65, P(B) = 0.55 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 0.85
2) 0.35
3) 1.85
4) 1.35

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 awa

PA) = 0.65

P(B) = 0.55

P(A∩B) = 0.35

P(A∪B)= P(A) + P(B) - P(A∩B)

= 0.65 + 0.55 - 0.35

= 0.65 + 0.2

= 0.85

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

1) 0
2) 14' title="

\frac{1}{4}

"/>

\frac{1}{4}

3) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

4) 1

Answer: 1

SOLUTION 1 :

Probability of an impossible event.

P(Ø) = 0.

The probability that a student will score centum in mathematics is $\frac{4}{5}$ . The probability that be will not score centum is _____

1) 35 ' title="

\frac{3}{5}

"/>

\frac{3}{5}

2) 15 ' title="

\frac{1}{5}

"/>

\frac{1}{5}

3) 55 ' title="

\frac{5}{5}

"/>

\frac{5}{5}

4) 65 ' title="

\frac{6}{5}

"/>

\frac{6}{5}

Answer: 2

SOLUTION 1 :

P(M) = $\frac{4}{5}$

w.k.t P(M) + P(M¯) = 1

$\frac{4}{5}$ + P(M¯) = 1

P(M¯) = 1 - $\frac{4}{5}$

P(M¯) = 5-4 / 5

= $\frac{1}{5}$

Ans = $\frac{1}{5}$

There are 7 defective items in a sample of 12 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 127 ' title="

\frac{12}{7}

"/>

\frac{12}{7}

2) 12 ' title="

\frac{1}{2}

"/>

\frac{1}{2}

3) 712 ' title="

\frac{7}{12}

"/>

\frac{7}{12}

4) 512 ' title="

\frac{5}{12}

"/>

\frac{5}{12}

Answer: 4

SOLUTION 1 :

Given:

n(S) = 12

Number of non-defective item = 12 - 7

n(A) = 5.

P(A) = $\frac{n(A)}{n(S)}$ = $\frac{5}{12}$ = $\frac{5}{12}$

Ans = $\frac{5}{12}$ .

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

1) 1
2) 12' title="

\frac{1}{2}

"/>

\frac{1}{2}

3) 18' title="

\frac{1}{8}

"/>

\frac{1}{8}

4) 0

Answer: 1

SOLUTION 1 :

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

Ans= 1

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) B
2) C
3) D
4) A

Answer: 4

SOLUTION 1 :

P(¯A∩B) = p(B) - P(A∩B)

Ans = (A) = P(B) - P(A∩B)

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) D
3) C
4) A

Answer: 2

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

10)

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

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

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

Answer: 2

SOLUTION 1 :

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

Ans (D) = 0 < P < 1