Probability - MCQ 5 | 20 Questions MCQ Test

QUESTION: 1

The probability of two persons of passing the interview are 1/3 and 3/5. Then calculate the probability that only one of them pass the interview ?

A.
7/15
B.
8/15
C.
11/15
D.
13/15

Solution:

PF + FP (P = pass, F = fail)
1/3*2/5 + 2/3*3/5 = 8/15

QUESTION: 2

Among a group of 5 boys and 6 girls, 4 members is to be selected for an event. Find the probability that at least one boy is selected ?

A.
17/22
B.
19/22
C.
21/22
D.
15/22

Solution:

sol = 1 – no boy is selected
1 – 6c4/11c4 = 21/22

QUESTION: 3

The probability that the problem will be solved by three persons are 1/2, 1/3 and 1/6. Find the probability that the problem is solved ?

A.
11/18
B.
13/18
C.
15/18
D.
17/18

Solution:

1 – 1/2*2/3*5/6 = 13/18

QUESTION: 4

A urn contains 4 red balls, 5 green balls and 6 white balls, If one ball is drawn at random, find the probability that it is neither red nor white ?

A.
1/3
B.
1/4
C.
1/5
D.
2/3

Solution:

5c1/15c1 = 1/3

QUESTION: 5

An elevator starts with 4 passenger and stops at 7 floors of an apartment. Find the probability that all 4 passengers travel to different floor ?

A.
110/343
B.
120/343
C.
18/49
D.
139/343

Solution:

Total number of outcomes = 7*7*7*7
Favourable outcome = 7*6*5*4
P = (7*6*5*4)/7*7*7*7 = 120/343

QUESTION: 6

A five digit number is formed from the numbers 1,3,5,7,8 and 9 without repeating the numbers. Find the probability that the number is divisible by 5 ?

A.
1/4
B.
1/5
C.
1/6
D.
1/7

Solution:

Total number of outcome = 6*5*4*3*2
Favourable outcome = 5*4*3*2. So, P = 1/6

QUESTION: 7

From a deck of 52 cards, a card is selected and without replacing the card a new card is selected. Find out the probability that the first card is an ace and second card is a king ?

A.
4/52*3/51
B.
4/51*3/52
C.
4/52*4/51
D.
3/52*3/51

Solution:

4/52*4/51

QUESTION: 8

The probability that a person will be alive after 20 years is 1/4 and that of his wife is 2/5. Find out the probability that both are not alive after 20 years ?

A.
7/20
B.
9/20
C.
11/20
D.
13/20

Solution:

prob. That man is not alive = 3/4 and that of his wife = 3/5
Prob. That both will be dead = 3/4*3/5 = 9/20

QUESTION: 9

Three coins are tossed simultaneously.

Find out the probability that there is at least 2 heads ?

A.
1/2
B.
1/4
C.
1/6
D.
1/8

Solution:

= Total outcomes = {HHH,HTH,HHT,THH,TTT,TTH,THT,HTT}
Favourable outcome = HHH, HTH, HHT,THH
Prob = 4/8 = 1/2

QUESTION: 10

Three coins are tossed simultaneously.

Find the probability that there is exactly two tails ?

A.
3/8
B.
5/8
C.
7/8
D.
1/8

Solution:

Favourable outcome = TTH, THT, HTT
So, prob. = 3/8

QUESTION: 11

An urn contain 6 orange, 4 green,3 pink and 4 black balls

If 3 balls are picked at random, what is the probability that all are pink ?

A.
2/650
B.
1/680
C.
4/630
D.
3/680

Solution:

17C3 = 17*16*15/3*2*1 = 4080/6 = 680
3C3 = 1
P = 1/680

QUESTION: 12

An urn contain 6 orange, 4 green,3 pink and 4 black balls

If 5 balls are picked at random, what is the probability that none are orange ?

A.
33/442
B.
442/33
C.
15/167
D.
23/235

Solution:

17C5 = 17*16*15*14*13/5*4*3*2*1 = 742560/120 = 6188
11C5 = 11*10*9*8*7/5*4*3*2*1 = 55440/120 = 462
P = 462/6188 = 33/442

QUESTION: 13

An urn contain 6 orange, 4 green,3 pink and 4 black balls.

If 3 balls are drawn at random, what is the probability that 1 is green and the other 2 are black ?

A.
2/85
B.
4/87
C.
1/85
D.
3/85

Solution:

17C3 = 17*16*15/3*2*1 = 4080/6 = 680
4C1 × 4C2 = 4*4*3/2*1 = 24
P = 24/680 = 3/85

QUESTION: 14

There are 8 positive numbers and 6 negative numbers. 4 numbers are chosen at random and multiplied. Find the probability that the product is a positive number ?

A.
1001/505
B.
101/505
C.
505/1001
D.
450/965

Solution:

14C4 = 14*13*12*11/4*3*2*1 = 1001
4 No positive+4 no negative + (2 no positive * 2 no negative)
= 6C4 + 8C4 +(6C2 ×8C2) = 15+70+15*28 = 505
P = 505/1001

QUESTION: 15

A five digit number is formed with the digit 1,2,3,4 and 5 without repetition. Find the chance that the number is divisible by 5 ?

A.
1/4
B.
1/5
C.
1/3
D.
1/2

Solution:

5! = 5*4*3*2*1 = 120
4! = 4*3*2*1 = 24
P = 24/120 = 1/5

QUESTION: 16

A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are green?

A.
1/78
B.
2/75
C.
4/89
D.
None

Solution:

13C2 = 13*12/2 =78
2C2 = 1
P = 1/78

QUESTION: 17

If You toss a coin and roll a die. What is the probability of getting a head and a 3 on the die?

A.
1/10
B.
1/8
C.
1/12
D.
2/3

Solution:

1/2 * 1/6 = 1/12

QUESTION: 18

From a pack of 52 cards, 3 cards are drawn. What is the probability that one is ace, one is queen and one is jack?

A.
12/5520
B.
15/4525
C.
13/5005
D.
16/5525

Solution:

=4C1×4C1×4C1 / 52C3
=4×4×4 / 22100
=16/5525

QUESTION: 19

Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other dice.

A.
10/28
B.
11/38
C.
11/36
D.
12/35

Solution:

n(S) = 36
n(E) = (2,3),(2,6),(4,3),(4,6),(6,3),(6,6),(3,2),(6,2),(3,4),(6,4),(3,6)
P = 11/36

QUESTION: 20

Two dice are tossed. The probability that the total score is a prime number is

A.
5/12
B.
7/12
C.
6/11
D.
5/7

Solution:

E = (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5)
n(E) = 15
n(S) = 6*6 = 36
P = 15/36 = 5/12