Question

In a diving competition, each diver has a 20% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score ? (Assume that each diver can perform only one dive per turn.)

• A. $\frac{4}{25}$
• B. $\frac{16}{25}$
• C. $\frac{16}{125}$
• D. $\frac{8}{125}$

Answer 1

The correct option is C $\frac{16}{125}$

In a diving competition, each diver has a 20% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive her chance of receiving a perfect score

Probability of all the three Dives being Imperfect dives

$=$ $\frac{4}{5}$$\frac{4}{5}$$\frac{4}{5}$=$\frac{64}{125}$

and Probability of First dive being Imperfect and Second being Perfect dive = $\frac{4}{5}\frac{1}{5}=\frac{4}{25}$

and Probability of First dive being Perfect dive = $\frac{1}{5}$

I.e. Total Unfavourable probability =$\frac{64}{125}$+$\frac{4}{25}$+$\frac{1}{5}$ = $\frac{109}{125}$

i.e. Total Favorable probability$=1$-$\frac{109}{125}$ = $\frac{16}{125}$