Question

On tossing three coins simultaneously, the probability of getting at least one head and tail is $\frac{x}{4}$.
The value of x is ___ .

Answer 1

Let E be the event of getting at least one head and tail. The complimentary event in this case is not getting one head and tail. The two outcomes of this event are HHH and TTT. Hence, P(not E) = $\frac{2}{8}$ = $\frac{1}{4}$.
The required probability P(E) = 1 – $\frac{1}{4}$ = $\frac{3}{4}$.