5. In a bag of 30 cookies, there are 12 chocolate chip, 4 double chocolate chip, 5 peanut butter, 3 sugar, and 6 mint chocolate cookies. If Sarah reaches in and takes a 2 cookies and eats them, what is the probability of her picking a chocolate chip cookie and then a peanut butter cookie? Are these events independent or dependent?
2/29
60/ 870
3/6
12/16

Step-by-step explanation: Given that in a bag of 30 cookies, there are 12 chocolate chip, 4 double chocolate chip, 5 peanut butter, 3 sugar, and 6 mint chocolate cookies.

Sarah reaches in and takes a 2 cookies and eats them.

We are to find the probability that she picked a chocolate chip cookie and then a peanut butter cookie. Also, to check whether these events are independent or dependent.

Let A denotes the event that Sarah picks a chocolate chip cookie and B denotes the event that Sarah picks a peanut butter cookie.

So, the probabilities of events A and B are

[tex]P(A)=\dfrac{^{12}C_1}{^{30}C_1}=\dfrac{12}{30}=\dfrac{2}{5},\\\\\\P(B)=\dfrac{^5C_1}{^{29}C_1}=\dfrac{5}{29}.[/tex]

Since the number of total cookies is reduced by one after Sarah picked and ate chocolate chip cookie, so

event B is dependent on event A.

Therefore, the events are dependent and the probability that Sarah picked a chocolate chip cookie and then a peanut butter cookie is

[tex]P(A)\times P(B)=\dfrac{2}{5}\times\dfrac{5}{29}=\dfrac{2}{29}.[/tex]

Thus, the required probability is [tex]\dfrac{2}{29}[/tex] and the events are dependent.

Option (A) is CORRECT.