Sasi Math (Revised for 1024)

Scroll:Probability >> Multiple choice question >> mcq (4521)

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 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) 512 ' title="

\frac{5}{12}

"/>

\frac{5}{12}

2) 127 ' title="

\frac{12}{7}

"/>

\frac{12}{7}

3) 12 ' title="

\frac{1}{2}

"/>

\frac{1}{2}

4) 712 ' title="

\frac{7}{12}

"/>

\frac{7}{12}

( )

If A and B are two events such that P(A) = 0.75, P(B) = 0.65 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 2.05
2) 1.55
3) 0.55
4) 1.05

( )

There are 5 defective items in a sample of 13 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 513 ' title="

\frac{5}{13}

"/>

\frac{5}{13}

2) 813 ' title="

\frac{8}{13}

"/>

\frac{8}{13}

3) 135 ' title="

\frac{13}{5}

"/>

\frac{13}{5}

4) 413 ' title="

\frac{4}{13}

"/>

\frac{4}{13}

( )

If A and B are two events such that P(A) = 0.75, P(B) = 0.85 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 2.25
2) 1.25
3) 0.75
4) 1.75

( )

There are 4 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) 14 ' title="

\frac{1}{4}

"/>

\frac{1}{4}

2) 124 ' title="

\frac{12}{4}

"/>

\frac{12}{4}

3) 412 ' title="

\frac{4}{12}

"/>

\frac{4}{12}

4) 23 ' title="

\frac{2}{3}

"/>

\frac{2}{3}

( )

If A and B are two events such that P(A) = 0.85, P(B) = 0.55 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 1.05
2) 1.55
3) 2.05
4) 0.55

( )

There are 3 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) 221 ' title="

\frac{2}{21}

"/>

\frac{2}{21}

2) 67 ' title="

\frac{6}{7}

"/>

\frac{6}{7}

3) 213 ' title="

\frac{21}{3}

"/>

\frac{21}{3}

4) 321 ' title="

\frac{3}{21}

"/>

\frac{3}{21}

( )

If A and B are two events such that P(A) = 0.55, P(B) = 0.95 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 1.15
2) 2.15
3) 0.65
4) 1.65

( )

There are 6 defective items in a sample of 15 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 615 ' title="

\frac{6}{15}

"/>

\frac{6}{15}

2) 13 ' title="

\frac{1}{3}

"/>

\frac{1}{3}

3) 35 ' title="

\frac{3}{5}

"/>

\frac{3}{5}

4) 156 ' title="

\frac{15}{6}

"/>

\frac{15}{6}

( )

10)

If A and B are two events such that P(A) = 0.85, P(B) = 0.95 and P(A∩B) = 0.15, then P(A∪B) = _______

1) 2.15
2) 1.65
3) 1.15
4) 2.65

( )

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) 512 ' title="

\frac{5}{12}

"/>

\frac{5}{12}

2) 712 ' title="

\frac{7}{12}

"/>

\frac{7}{12}

3) 127 ' title="

\frac{12}{7}

"/>

\frac{12}{7}

4) 12 ' title="

\frac{1}{2}

"/>

\frac{1}{2}

Answer: 1

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 A and B are two events such that P(A) = 0.75, P(B) = 0.65 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 2.05
2) 1.05
3) 1.55
4) 0.55

Answer: 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 awa

PA) = 0.75

P(B) = 0.65

P(A∩B) = 0.35

P(A∪B)= P(A) + P(B) - P(A∩B)

= 0.75 + 0.65 - 0.35

= 0.75 + 0.3

= 1.05

There are 5 defective items in a sample of 13 items. One item is drawn at random. The probability that it is a non-defective item is _______

1) 813 ' title="

\frac{8}{13}

"/>

\frac{8}{13}

2) 413 ' title="

\frac{4}{13}

"/>

\frac{4}{13}

3) 135 ' title="

\frac{13}{5}

"/>

\frac{13}{5}

4) 513 ' title="

\frac{5}{13}

"/>

\frac{5}{13}

Answer: 1

SOLUTION 1 :

Given:

n(S) = 13

Number of non-defective item = 13 - 5

n(A) = 8.

P(A) = $\frac{n(A)}{n(S)}$ = $\frac{8}{13}$ = $\frac{8}{13}$

Ans = $\frac{8}{13}$ .

If A and B are two events such that P(A) = 0.75, P(B) = 0.85 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 1.75
2) 2.25
3) 1.25
4) 0.75

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) = 0.75

P(B) = 0.85

P(A∩B) = 0.35

P(A∪B)= P(A) + P(B) - P(A∩B)

= 0.75 + 0.85 - 0.35

= 0.75 + 0.5

= 1.25

There are 4 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) 124 ' title="

\frac{12}{4}

"/>

\frac{12}{4}

2) 14 ' title="

\frac{1}{4}

"/>

\frac{1}{4}

3) 412 ' title="

\frac{4}{12}

"/>

\frac{4}{12}

4) 23 ' title="

\frac{2}{3}

"/>

\frac{2}{3}

Answer: 4

SOLUTION 1 :

Given:

n(S) = 12

Number of non-defective item = 12 - 4

n(A) = 8.

P(A) = $\frac{n(A)}{n(S)}$ = $\frac{8}{12}$ = $\frac{2}{3}$

Ans = $\frac{2}{3}$ .

If A and B are two events such that P(A) = 0.85, P(B) = 0.55 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 1.55
2) 2.05
3) 1.05
4) 0.55

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) = 0.55

P(A∩B) = 0.35

P(A∪B)= P(A) + P(B) - P(A∩B)

= 0.85 + 0.55 - 0.35

= 0.85 + 0.2

= 1.05

There are 3 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) 321 ' title="

\frac{3}{21}

"/>

\frac{3}{21}

2) 67 ' title="

\frac{6}{7}

"/>

\frac{6}{7}

3) 221 ' title="

\frac{2}{21}

"/>

\frac{2}{21}

4) 213 ' title="

\frac{21}{3}

"/>

\frac{21}{3}

Answer: 2

SOLUTION 1 :

Given:

n(S) = 21

Number of non-defective item = 21 - 3

n(A) = 18.

P(A) = $\frac{n(A)}{n(S)}$ = $\frac{18}{21}$ = $\frac{6}{7}$

Ans = $\frac{6}{7}$ .

If A and B are two events such that P(A) = 0.55, P(B) = 0.95 and P(A∩B) = 0.35, then P(A∪B) = _______

1) 1.15
2) 1.65
3) 0.65
4) 2.15

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) = 0.55

P(B) = 0.95

P(A∩B) = 0.35

P(A∪B)= P(A) + P(B) - P(A∩B)

= 0.55 + 0.95 - 0.35

= 0.55 + 0.6

= 1.15

There are 6 defective items in a sample of 15 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) 615 ' title="

\frac{6}{15}

"/>

\frac{6}{15}

3) 156 ' title="

\frac{15}{6}

"/>

\frac{15}{6}

4) 35 ' title="

\frac{3}{5}

"/>

\frac{3}{5}

Answer: 4

SOLUTION 1 :

Given:

n(S) = 15

Number of non-defective item = 15 - 6

n(A) = 9.

P(A) = $\frac{n(A)}{n(S)}$ = $\frac{9}{15}$ = $\frac{3}{5}$

Ans = $\frac{3}{5}$ .

10)

If A and B are two events such that P(A) = 0.85, P(B) = 0.95 and P(A∩B) = 0.15, then P(A∪B) = _______

1) 2.65
2) 1.65
3) 1.15
4) 2.15

Answer: 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 awa

PA) = 0.85

P(B) = 0.95

P(A∩B) = 0.15

P(A∪B)= P(A) + P(B) - P(A∩B)

= 0.85 + 0.95 - 0.15

= 0.85 + 0.8

= 1.65