Probability Test

Result

Probability Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

You are given a box with 25 cards in it. 10 of these cards have letter "I" printed on them and the other 15 have the letter "T" printed on them. If you pick up 3 cards one by one at random and keep them in the same order, the probability of making the word I.I.T. is

A
9/80

B
1/8

C
9/27

D
9/92

Solution

Required Probability,
P('I' first Draw)+P('I' first Draw) + P('T' first Draw)
= [10C1]/[25C1] + [9C1]/[24C1] + [15C1]/[23C1]
=[10/25] × [9/24] × [15/23]
= 1350/13800
= 45/460
= 9/92
Question 2
1 / -0

A person draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail in the first two draws is

A
9/64

B
1/64

C
1/16

D
9/16

Solution

Required probability = π
Question 3
1 / -0

From each of two married couples, one of the partners is selected randomly. The probability that those selected are of the opposite sex is

A
1/2

B
1/4

C
7/8

D
1/16

Solution

number of favourable outcomes/ total number of outcomes

= ½
Question 4
1 / -0

A bag contains 15 white and 4 green balls. One ball is drawn at random. The probability that it is green is

A
7/5

B
4/7

C
2/3

D
4/19

Solution

Total number of balls = 15 + 4 = 19
Number of green balls = 4

Required probability = 4/19
Question 5
1 / -0

Two fair dice are thrown. Let X be the event that the first die shows an even number and Y be the event that the second die shows an odd number. The two events X and Y are

A
mutually exclusive

B
independent and mutually exclusive

C
dependent

D
independent

Solution

Events are independent but mutually exclusive as the outcomes of both events are different.