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3. Suppose a group of four cookies will be selected from a jar that has 12 chocolate-chip and 10 oatmeal cookies. (a) What is the probability all four cookies are chocolate-chip? (b) What is the probability the group has at most three chocolate-chip cookies? Interpret this result. (c) If only two cookies are selected at random, what is the probability the group has one of each flavor of cookie?

3. Suppose a group of four cookies will be selected from a jar that has 12 chocolate-chip and 10 oatmeal cookies. (a) What is the probability all four cookies are chocolate-chip? (b) What is the probability the group has at most three chocolate-chip cookies? Interpret this result. (c) If only two cookies are selected at random, what is the probability the group has one of each flavor of cookie?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 3 Please solve with simple probability rules
**Probability of Selecting Cookies from a Jar** Consider a situation where a group of four cookies will be selected from a jar containing 12 chocolate-chip cookies and 10 oatmeal cookies. We are interested in finding various probabilities related to the selection of these cookies. **Problem:** - A total of 22 cookies: 12 chocolate-chip and 10 oatmeal. - A group of four cookies is selected randomly. **Question (a):** What is the probability all four cookies are chocolate-chip? **Question (b):** What is the probability the group has at most three chocolate-chip cookies? Interpret this result. **Question (c):** If only two cookies are selected at random, what is the probability the group has one of each flavor of cookie? --- ### Solution: #### (a) Probability all four cookies are chocolate-chip: To determine this probability, we calculate the combination of choosing 4 chocolate-chip cookies from the 12 available, divided by the combination of choosing 4 cookies from all 22 cookies. #### (b) Probability the group has at most three chocolate-chip cookies: This involves finding the probability for 0, 1, 2, and 3 chocolate-chip cookies in the group. This is done by summing the respective probabilities for these scenarios. #### (c) Probability the group has one of each flavor (two cookies selected): We need to find the probability that among the two cookies selected, one is chocolate-chip and one is oatmeal. ### Diagrams/Graphs: There are no diagrams or graphs provided in the image text. --- These calculations help understand the outcomes and likelihoods when selecting a random group of cookies from a jar with different varieties.
Transcribed Image Text:**Probability of Selecting Cookies from a Jar** Consider a situation where a group of four cookies will be selected from a jar containing 12 chocolate-chip cookies and 10 oatmeal cookies. We are interested in finding various probabilities related to the selection of these cookies. **Problem:** - A total of 22 cookies: 12 chocolate-chip and 10 oatmeal. - A group of four cookies is selected randomly. **Question (a):** What is the probability all four cookies are chocolate-chip? **Question (b):** What is the probability the group has at most three chocolate-chip cookies? Interpret this result. **Question (c):** If only two cookies are selected at random, what is the probability the group has one of each flavor of cookie? --- ### Solution: #### (a) Probability all four cookies are chocolate-chip: To determine this probability, we calculate the combination of choosing 4 chocolate-chip cookies from the 12 available, divided by the combination of choosing 4 cookies from all 22 cookies. #### (b) Probability the group has at most three chocolate-chip cookies: This involves finding the probability for 0, 1, 2, and 3 chocolate-chip cookies in the group. This is done by summing the respective probabilities for these scenarios. #### (c) Probability the group has one of each flavor (two cookies selected): We need to find the probability that among the two cookies selected, one is chocolate-chip and one is oatmeal. ### Diagrams/Graphs: There are no diagrams or graphs provided in the image text. --- These calculations help understand the outcomes and likelihoods when selecting a random group of cookies from a jar with different varieties.
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