Probability Theory - 1 - Free MCQ Practice Test with solutions, SSC CGL

Here S = {HH, HT, TH, TT}
Let E = event of getting at least one head = {HT, TH, HH}

Let S be the sample space
Then,

Let number of balls = (6+8)=14
Number of white balls = 8P (drawing a white ball)
= 8/14 = 4/7

Let S be the sample space

Let E = event of getting 1 spade and 1 heart
∴ n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13

Here, n(S) = 52
Let E = event of getting a queen of club or a king of heart
Then, n(E) = 2

Total number of balls
= (2 + 3 + 2)
= 7
Let S be the sample space
Then, n(S) = Number of ways of drawing 2 balls out of 7

Let E = Event of 2 balls, none of which is blue
∴ n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls

In two throws of a dice, n(S) = (6 x 6) = 36
Let E = event of getting a sum
= {(3, 6), (4, 5), (5, 4), (6, 3)}

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36

Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Clearly, n(S) = (6 x 6) = 36
Let E = Event that the sum is a prime number.Then
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)}