Question

chapter 3: 3.2 independent and mutually exclusive events homework score: 10/15 answered: 10/14 question 11 ivan buys a bag of cookies that contains 6 chocolate chip cookies, 9 peanut butter cookies, 4 sugar cookies and 7 oatmeal cookies. what is the probability that ivan randomly selects a sugar cookie from the bag, eats it, then randomly selects a peanut butter cookie? probability = (round your answer to 4 decimal places.) submit question

Explanation:

Step1: Calculate total number of cookies initially

The total number of cookies in the bag initially is the sum of all types of cookies. So, $6 + 9+4 + 7=26$ cookies.

Step2: Calculate probability of selecting a sugar - cookie first

The probability of selecting a sugar - cookie first, $P(S_1)=\frac{4}{26}$.

Step3: Calculate number of cookies left after eating a sugar - cookie

After eating a sugar - cookie, the number of remaining cookies is $26 - 1=25$ cookies.

Step4: Calculate probability of selecting a peanut - butter cookie second

The number of peanut - butter cookies is 9. So the probability of selecting a peanut - butter cookie second given that a sugar - cookie was selected first, $P(PB_2|S_1)=\frac{9}{25}$.

Step5: Use the multiplication rule for dependent events

The probability of both events happening is $P = P(S_1)\times P(PB_2|S_1)=\frac{4}{26}\times\frac{9}{25}=\frac{36}{650}= 0.0554$

Answer:

$0.0554$