Question

The probability that Dhoni will hit century in every ODI matches he lays is $\frac{1}{5}$. If he plays $6$ matches in World Cup 2011, the probability that he will score century in all the $6$ test matches is:

• A. $\frac{1}{3125}$
• B. $\frac{5}{3125}$
• C. $\frac{4096}{15625}$
• D. $\frac{1555}{3125}$

Answer 1

The correct option is A $\frac{1}{3125}$

Probability of getting a century, $p=\frac{1}{5}$

Probability of not getting a century, $q=\frac{4}{5}$

$\Rightarrow$ Total no. of match $=6$

By Bernoulli's equation,

$\Rightarrow p={}^n{C}_r{p}^r{q}^{n-r}$

p ( getting atleast $1$ ) $={}^6{C}_6{\left(\frac{1}{5}\right)}^6$

$=\frac{5}{15625}$

$=\frac{1}{3125}$

Hence, the answer is $\frac{1}{3125}.$