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

3. In each of the following experiments, write the sample space S, number of sample point n (S), events A, B and n(A), n(B). A coin is tossed three times. A is the event that head appears once, B is the event that head appears at the most twice.

Since a coin is tossed three times

∴ Sample space = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

∴ n(S) = 8

Let A = Event that the head appears once.

∴ A = {HTT, THT, TTH }

∴ n(A) = 3

Let B = Event that the head appears at the most twice

∴ B = {HHT, HTH, HTT, THH, THT, TTH, TTT}

∴ n(B) = 7