Question

part two - short answer! make sure to show all work in order to receive credit!
#1. michael has 12 snickers, 13 milky ways, 9 twix, and 6 mars bars. he randomly chooses a candy bar, eats it, and then chooses another.
a. is this an example of an independent or dependent event? explain how you know
b. find the p(snickers than mars bar)

Explanation:

Part A

To determine if the events are independent or dependent, we analyze the effect of the first event (choosing and eating a candy bar) on the second event (choosing another candy bar). In independent events, the outcome of one event does not affect the outcome of the other. In dependent events, the outcome of one event affects the outcome of the next because the sample space changes. Here, when Michael eats the first candy bar, the total number of candy bars decreases, and the probability of choosing the second candy bar is affected by the first choice. So, the events are dependent.

Step1: Calculate total number of candy bars initially.

Total candy bars = 12 (Snickers) + 13 (Milky Ways) + 9 (Twix) + 8 (Mars Bars) = 12 + 13 + 9 + 8 = 42.

Step2: Probability of choosing a Snickers first.

P(Snickers first) = $\frac{\text{Number of Snickers}}{\text{Total number of candy bars}}$ = $\frac{12}{42}$.

Step3: After eating a Snickers, calculate new total number of candy bars and number of Mars Bars.

New total candy bars = 42 - 1 = 41.
Number of Mars Bars remains 8.

Step4: Probability of choosing a Mars Bar second (given a Snickers was chosen first).

P(Mars Bar second | Snickers first) = $\frac{\text{Number of Mars Bars}}{\text{New total number of candy bars}}$ = $\frac{8}{41}$.

Step5: Calculate the probability of Snickers then Mars Bar (using multiplication rule for dependent events).

P(Snickers then Mars Bar) = P(Snickers first) × P(Mars Bar second | Snickers first) = $\frac{12}{42}$ × $\frac{8}{41}$.
Simplify $\frac{12}{42}$ to $\frac{2}{7}$. Then, $\frac{2}{7}$ × $\frac{8}{41}$ = $\frac{16}{287}$.

Answer:

This is a Dependent Event. Because after choosing and eating the first candy bar, the total number of candy bars available for the second choice is reduced, which affects the probability of the second event.

Part B