uppose you have a cookie jar that contains 10 chocolate chip cookies and 39 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
uppose you have a cookie jar that contains 10 chocolate chip cookies and 39 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 calculate the probability:
Step 1: Calculate the total number of cookies. You have 10 chocolate chip cookies and 39 oatmeal cookies, so the total number of cookies is 10 + 39 = 49 cookies.
Step 2: Calculate the probability of drawing a chocolate chip cookie on the first draw. The probability of drawing a chocolate chip cookie on the first draw is the number of chocolate chip cookies divided by the total number of cookies, which is 10/49 = 0.2041.
Step 3: Calculate the new total number of cookies and the new number of chocolate chip cookies after one has been drawn. After drawing one chocolate chip cookie, you have 9 chocolate chip cookies left and 48 total cookies left.
Step 4: Calculate the probability of drawing a chocolate chip cookie on the second draw. The probability of drawing a chocolate chip cookie on the second draw is the new number of chocolate chip cookies divided by the new total number of cookies, which is 9/48 = 0.1875.
Step 5: Calculate the probability of both events happening. The probability of both events happening is the probability of the first event multiplied by the probability of the second event, which is 0.2041 * 0.1875 = 0.0383.
So, the probability that both cookies drawn are chocolate chip is approximately 0.04 or 4% when rounded to two decimal places.
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