Question

In a simultaneous toss of four coins, what is the probability of getting exactly three heads

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. None of these

Answer 1

The correct option is C

$\frac{1}{4}$

Explanation for the correct option.

Find the probability.

When four coins are tossed, total possible outcomes is given by sample space $S$ as

$$\begin{gathered} S=\left\{HHHH,HHHT,HHTH,HHTT,HTHH,HTHT,HTTH,HTTT, \\ THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT\right\} \end{gathered}$$.

So the total number of outcomes is $n\left(S\right)=16$.

Let $A$ be the event of head occurring exactly three times, then

$A=\left\{HHHT,HHTH,HTHH,THHH\right\}$

So the number of favorable outcomes is $n\left(A\right)=4$.

So the probability that exactly three heads occurs

$\begin{array}{rcl}P\left(A\right)& =& \frac{n\left(A\right)}{n\left(S\right)}\\ & =& \frac{4}{16}\\ & =& \frac{1}{4}\end{array}$

Hence, the correct option is C.