Question

A box contains 4 chocolates and 1 fruit chew. Clark and Chloe take turns drawing a treat out from the box without replacement. Whoever draws the fruit chew wins. Clark draws first. What is the probibility that Chloe wins. The answer is 2/5. Can you please explain why?

Answer 1

hhhhhhhhhhhhhhhhhhhhhh

Answer 2

Answer:

The Probability that Chloe wins is $\dfrac{2}{5}$

Step-by-step explanation:

We are given 4 chocolates and 1 fruit chew.

this means we have total 5 choices.

Now Clark draws first. and there is no replacement that means if one treat is drawn it won't be counted again.

Now we need to find the probability that Chloe wins i.e. he draws out the fruit chew one.

Probability=$\dfrac{4}{5}\times\dfrac{1}{4}+\dfrac{4}{5}\times \dfrac{3}{4}\times \dfrac{2}{3}\times \dfrac{1}{2}$

where the first term in the summation i.e.  $\dfrac{4}{5}\times\dfrac{1}{4}$ shows that in the first turn Clark draws a chocolate box out of the 5 boxes and Chloe in his first turn draws a fruit chew and wins.

whereas second term in the summation shows that Chloe draws a fruit chew in his second draw.

Probability=$\dfrac{1}{5}+\dfrac{1}{5}=\dfrac{2}{5}$

Hence, the Probability that Chloe wins is $\dfrac{2}{5}$