Suppose you have a cookie jar that contains 13 chocolate chip cookies and 24 oatmeal cookies. If you reach in the jar and pull out 2 cookies at random, find the probability that both are chocolate chip. Express answer to two decimal places.
Question
Suppose you have a cookie jar that contains 13 chocolate chip cookies and 24 oatmeal cookies. If you reach in the jar and pull out 2 cookies at random, find the probability that both are chocolate chip. Express answer to two decimal places.
Solution
Sure, here's how you can solve this problem:
Step 1: Calculate the total number of cookies in the jar. This is the sum of the chocolate chip cookies and the oatmeal cookies, which is 13 + 24 = 37 cookies.
Step 2: Calculate the probability of drawing a chocolate chip cookie on the first draw. This is the number of chocolate chip cookies divided by the total number of cookies, which is 13/37.
Step 3: If you don't replace the first cookie, there are now 36 cookies left in the jar, and only 12 of them are chocolate chip. So, the probability of drawing a chocolate chip cookie on the second draw is 12/36.
Step 4: The probability of both events happening (drawing a chocolate chip cookie on the first draw AND drawing a chocolate chip cookie on the second draw) is the product of the probabilities of each event. So, the probability of drawing two chocolate chip cookies in a row is (13/37) * (12/36).
Step 5: Calculate this product to get the final answer. The answer is approximately 0.095 or 9.5% when expressed as a percentage to two decimal places.
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