Question

If three coins are tossed simultaneously, then the probability of getting at least one head and tail is _____.

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{3}{4}$

Given, a coin is tossed 3 times.

Total possible outcomes = {HHH, HHT, HTT, HTH, THH, TTH, THT, TTT} (where H = Heads, T= Tails)
Total no. of possible outcomes = 8
Favourable outcomes (getting at least one head and tail) = {HHT, HTT, HTH, THH, TTH, THT}
No. of favorable outcomes = 6
Probability of an event $E$,
$P\left(E\right)=\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

$\Rightarrow$ P (getting at least one head and tail) = $\frac{6}{8}$ = $\frac{3}{4}$
$\therefore$ The probability of getting at least one head and a tail is $\frac{3}{4}$.