(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
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Question 3.1 Please solve with simple probability rules
### Probability of Selecting Cookies

Consider a jar that contains 12 chocolate-chip cookies and 10 oatmeal cookies. We are interested in selecting cookies from this jar and calculating various probabilities.

#### Problem 3:
Suppose a group of four cookies will be selected from this jar.

**(a) What is the probability all four cookies are chocolate-chip?**

To determine this, we need to find the probability of selecting 4 chocolate-chip cookies out of the 12 available.

**(b) What is the probability the group has at most three chocolate-chip cookies? Interpret this result.**

This part asks for the probability of ending up with 0, 1, 2, or 3 chocolate-chip cookies in the selected group of 4 cookies. Calculate the probability for each scenario and sum them up to find the total.

Interpretation: This result helps in understanding the likelihood of having a mixture of chocolate-chip and oatmeal cookies in a group of 4 cookies.

**(c) If only two cookies are selected at random, what is the probability the group has one of each flavor of cookie?**

Here we need to find the probability of selecting one chocolate-chip cookie and one oatmeal cookie out of the 2 selected cookies.

Understanding these probabilities helps in determining the chances of various outcomes when selecting cookies from a jar containing two types of cookies.
Transcribed Image Text:### Probability of Selecting Cookies Consider a jar that contains 12 chocolate-chip cookies and 10 oatmeal cookies. We are interested in selecting cookies from this jar and calculating various probabilities. #### Problem 3: Suppose a group of four cookies will be selected from this jar. **(a) What is the probability all four cookies are chocolate-chip?** To determine this, we need to find the probability of selecting 4 chocolate-chip cookies out of the 12 available. **(b) What is the probability the group has at most three chocolate-chip cookies? Interpret this result.** This part asks for the probability of ending up with 0, 1, 2, or 3 chocolate-chip cookies in the selected group of 4 cookies. Calculate the probability for each scenario and sum them up to find the total. Interpretation: This result helps in understanding the likelihood of having a mixture of chocolate-chip and oatmeal cookies in a group of 4 cookies. **(c) If only two cookies are selected at random, what is the probability the group has one of each flavor of cookie?** Here we need to find the probability of selecting one chocolate-chip cookie and one oatmeal cookie out of the 2 selected cookies. Understanding these probabilities helps in determining the chances of various outcomes when selecting cookies from a jar containing two types of cookies.
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