Question

Peter and Mary take turns throwing one dart at the dartboard. Peterhits the bulls eye with probabilitypand Mary hits the bullseye with probabilityr.Whoever hits the bullseye first wins. Suppose Peter throws the first dart.(a) What is the probability that Mary wins

Answer 1

Answer:

$P(Mary) = (1 - p) * r$

Step-by-step explanation:

Given

$p \to$ Peter hits

$r \to$ Mary hits

Required

The probability that Mary wins

From the question, we understand that Peter throws the first.

If Mary is to win, then Peter has to lose his throw

Using the complement rule, the probability that Peter misses is:

$p' = 1 - p$

So, the probability that Mary wins is:

$P(Mary) = p' * r$

This gives:

$P(Mary) = (1 - p) * r$