Question

Two unbiased coins are tossed simultaneously. Find the probability of getting

a) no heads

b) at most one tail.

Answer 1

When two coins are tossed simultaneously, all possible outcomes are S = {HH, HT, TH, TT}.

Total number of elements in sample space = n(S) = 4

a) Let E be the event of getting no heads

E = {TT}; n(E) = 1

P(E) = $\frac{n\left(E\right)}{n\left(S\right)}$ =$\frac{1}{4}$

b) Let F be the event of getting at most one tail.

F = { HH, HT, TH}; n(F) = 3

P(F) = $\frac{n\left(F\right)}{n\left(S\right)}$ = $\frac{3}{4}$