In the following experiment write the sample space A, number of sample point n(S), event A, B, C and n(A), n(B), n(C). A die is thrown. A is the event that prime number comes up, B is the event that the number is divisible by three comes up, C is the event that the perfect square comes up.

Solution:

Since a die is thrown,

Sample Space = { 1, 2, 3, 4, 5, 6}

∴ n(S) = 6

Let  A = Event of getting a prime number.

∴ A = {2, 3, 5}

∴ n(A) = 3

Let B =  Event of getting a number divisible by 3

∴ B = {3, 6}

∴ n(B) = 2

Let C = Event of getting a perfect square comes up

∴ C = {1, 4}

∴ n(C) = 2

In the following experiment, write the sample space S, number of sample point n(S), event A, B, n(A), n(B). Two coins are tossed, A is the event of getting at most one head, B is the event of getting both heads.

Solution:

Since two coins are tossed

∴ Sample space = {HH, HT, TH, TT}

∴ n(S) = 4

Let A = Event of getting atmost one head

A = { HT, TH, TT}

∴ n(A) = 3

Let B =  Event of getting both heads

∴B = {HH}

∴ n(B) = 1