Probability Test

Result

Probability Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

Two dice, A and B, are rolled at the same time. The sum of the two numbers obtained is 7. What is the probability that the number obtained on die A is greater than that obtained on die B.

A
2/3

B
1/2

C
3/4

D
4/5

Solution

Let the event of getting a bigger number on A than on B be Q.
There are six ways to get a sum of 7 when two dice are rolled = (A, B) = {(2, 5), (1, 6), (3, 4), (5, 2),(4, 3), (6,1)}

Among these, there are three cases in which the number on A is greater than that on B: {(5, 2), (6, 1), (4, 3)}
Q = {(5, 2), (6, 1), (4, 3)}

Therefore, number of favourable case = 3
Total number of ways of getting a sum of 7 = 6

Required probability = 3/6 = 1/2
Question 2
1 / -0

In a pack of cards numbered from 1 to 100, how many favourable outcomes are there for picking a card containing a number that is divisible by 5?

A
19

B
10

C
20

D
9

Solution

Let A be the event of picking a card containing a number divisible by 5.
So, A = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100}
Therefore, number of favourable outcomes = 20
Question 3
1 / -0

There are 6 blue, 5 red, 3 orange and 2 yellow balls in a box. A ball is drawn at random from the box. What is the probability that the ball selected is not orange?

A
13/16

B
3/4

C
3/16

D
1/4

Solution

Total number of balls = 6 + 5 + 3 + 2 = 16
Number of orange balls = 3

Therefore, number of balls which are not orange = 16 - 3 = 13
Required probability = 13/16
Question 4
1 / -0

An anti-aircraft gun can fire only 4 shots at an enemy plane. The probabilities of hitting the plane in the first, second, third and fourth shots are 0.4, 0.3, 0.2 and 0.1, respectively. What is the probability that the plane gets hit?

A
0.698

B
0.424

C
0.302

D
None of these

Solution

Probability that the plane gets hit
= 1 − Probability of not hitting the plane
= 1 - (1 - 0.4)(1 - 0.3)(1 - 0.2)(1 - 0.1)
= 1 - (0.6)(0.7)(0.8)(0.9)
= 1 - 0.3024
= 0.6976 ≈ 0.698