A box contains 4 chocolates and 1 fruit chew. Clark and Chloe take turns drawing a treat out of the box without replacement. Whoever draws the fruit chew wins. Clark draws first. What is the probability that Chloe wins? Express your answer as a common fraction.
Let's find the probability that Clark wins, then subtract from 1.
Clark has a 1/5 chance of getting the fruit chew on the first draw.
Or a 4/5 chance of not.
If he has a 4/5 chance of not, then Chloe has a 3/4 chance of not.
Then Clark has a 1/3 chance of getting the fruit chew then.
Multiplying all of this, we get 1/5.
Or, if Clark has a 2/3 chance of not getting the fruit chew, then Chloe has a 1/2 chance, which means Clark must get the fruit chew at last.
Multiplying all of this gets us 1/5.
Adding the probability, we get 3/5
1-3/5 = 2/5
You are very welcome!