Question

The probability of getting at least one tail in 4 throws of a coin is

• A. $\frac{1}{16}$
• B. $\frac{1}{4}$
• C. $\frac{15}{16}$
• D. $\frac{1}{8}$

Answer 1

The correct option is C

$\frac{15}{16}$

Sample space
=$\left[\begin{array}{c}\\ TTHT,TTTH,TTTT,TTHH\\ THHT,THTH,THTT,THHH\\ HTHT,HTTH,HTTT,HTHH\\ HHHT,HHTH,HHTT,HHHH\end{array}\right]$
Total number of outcomes = 16
Favourable outcomes for getting all heads = { HHHH }
Number of favourable outcomes = 1
Probability of getting all heads = $\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$=$\frac{1}{16}$
P(atleast one tail) = 1 - P (Heads only)
$\Rightarrow$ P(Atleast one tail) = $1-\frac{1}{16}$
= $\frac{15}{16}$