Question

3
select the correct answer from each drop - down menu.
jeremy received a basket containing 8 red and 4 green apples.
when he randomly selects and eats two apples from the basket, these are
the probability that both of the apples jeremy eats are green is
events.

Explanation:

First Drop - Down (Type of Events)

When Jeremy selects and eats the first apple, the number of apples (and the number of green/red apples) changes for the second selection. So the outcome of the first event affects the second event. Such events are called dependent events.

Second Drop - Down (Probability Calculation)

Step 1: Probability of first green apple

The total number of apples initially is \(8 + 4=12\). The number of green apples is 4. So the probability of selecting a green apple first, \(P(G_1)=\frac{4}{12}=\frac{1}{3}\).

Step 2: Probability of second green apple (after first green is eaten)

After eating one green apple, the number of green apples left is \(4 - 1 = 3\) and the total number of apples left is \(12- 1=11\). So the probability of selecting a green apple second, \(P(G_2)=\frac{3}{11}\).

Step 3: Probability of both green apples

Since the two events are dependent, we multiply the probabilities: \(P(G_1\cap G_2)=P(G_1)\times P(G_2)=\frac{4}{12}\times\frac{3}{11}=\frac{12}{132}=\frac{1}{11}\approx0.0909\) (or \(\frac{1}{11}\) in fraction form).

Answer:

First drop - down: dependent
Second drop - down: \(\frac{1}{11}\) (or approximately \(0.09\) depending on the options, but the exact fraction is \(\frac{1}{11}\))