Question

A die is thrown four times. The probability of getting perfect square in at least one throw is

• A. $\frac{16}{81}$
• B. $\frac{65}{81}$
• C. $\frac{23}{81}$
• D. $\frac{58}{81}$

Answer 1

Answer: (B)

$\frac{65}{81}$

Answer 2

A die is thrown four time
$\therefore n=4$
$p$ (probability of getting perfect square i.e. 1,4$)$
Here,$p=\frac{2}{6}=\frac{1}{3}$
$q=1-p=1-\frac{1}{3}=\frac{2}{3}$
$\therefore$ Required probability
$=P(X \geq 1)=1-P(X=0)$
$=1-{ }^{4} C_{0}\left(\frac{1}{3}\right)^{0}\left(\frac{2}{3}\right)^{4}$
$=1-\frac{16}{81}=\frac{65}{81}$