Question

The probability of getting at least one tail, when four coins are tossed is .

• A. $\frac{1}{4}$
• B. $\frac{15}{16}$
• C. $\frac{3}{4}$
• D. $\frac{1}{16}$

Answer 1

The correct option is B $\frac{15}{16}$

$\text{Sample space}\left[\begin{array}{c}\\ TTHT,TTTH,TTTT,TTHH\\ THHT,THTH,THTT,THHH\\ HTHT,HTTH,HTTT,HTHH\\ HHHT,HHTH,HHTT,HHHH\end{array}\right]$

$\text{Total number of outcomes = 16}\text{Favourable outcomes for}\text{getting all heads = { HHHH }}\text{Number of favourable outcomes = 1}$

$\text{Probability of getting all heads}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{1}{16}$

$\text{P(Atleast one tail)}=1-\text{P (Heads only)}\Rightarrow \text{P(Atleast one tail)}=1-\frac{1}{16}=\frac{15}{16}$