Question

The probability that Sania wins Wimbledon tournaments final is $\frac{1}{3}$. If Sania Mirza plays $3$ round of Wimbledon final, the probability that she losses all the rounds is:

• A. $\frac{8}{27}$
• B. $\frac{19}{27}$
• C. $\frac{10}{27}$
• D. $\frac{17}{27}$

Answer 1

The correct option is A $\frac{8}{27}$

Probability that Sania wins Wimbledon tournament final $=\frac{1}{3}$

Probability that Sania losses $=\frac{2}{3}$

i.e, $p=\frac{1}{3}$ $q=\frac{2}{3}$

Total no. of rounds, $n=3$

P (She looses in all round ) , By Bernoullsi's theorm

$\Rightarrow P={}^n{C}_r{p}^r{q}^{n-r}={}^3{C}_0{\left(\frac{1}{3}\right)}^0{\left(\frac{2}{3}\right)}^3$

$=\frac{8}{27}.$

Hence, the answer is $\frac{8}{27}.$