Question

Susan has a bag with 5 mint sticks, 3 jelly treats, and 12 fruit tart chews. If she eats one piece every 8 minutes, what is the probability her first two pieces will be a fruit tart chew and a jelly treat and represent as a percent to the nearest tenth if necessary?
A.
63.2%
B.
0%
C.
9%
D.
9.5%

Answer 1

To determine the probability that Susan's first two pieces of candy will be a fruit tart chew followed by a jelly treat, we first need to find out the total number of candy pieces in the bag and then the probabilities of each event occurring in sequence.

1. **Total pieces of candy:**
- Mint sticks: 5
- Jelly treats: 3
- Fruit tart chews: 12

Total number of pieces = 5 + 3 + 12 = 20 pieces.

2. **Probability of the first piece being a fruit tart chew:**
- There are 12 fruit tart chews out of 20 total pieces.
\[
P(\text{first = fruit tart}) = \frac{12}{20} = 0.6
\]

3. **Probability of the second piece being a jelly treat given that the first was a fruit tart chew:**
- After eating one fruit tart chew, there will be 19 pieces left (20 - 1) with 3 of them being jelly treats.
\[
P(\text{second = jelly treat | first = fruit tart}) = \frac{3}{19}
\]

4. **Combined probability of both events:**
\[
P(\text{fruit tart first and jelly treat second}) = P(\text{first = fruit tart}) \times P(\text{second = jelly treat | first = fruit tart}) = \frac{12}{20} \times \frac{3}{19}
\]

Calculating this:
\[
P = \frac{12}{20} \times \frac{3}{19} = 0.6 \times \frac{3}{19} = \frac{1.8}{19}
\]

Now we convert \( \frac{1.8}{19} \) to a decimal:
\[
\frac{1.8}{19} \approx 0.0947368421
\]

To express this as a percentage:
\[
0.0947368421 \times 100 \approx 9.47368421\%
\]

Rounding to the nearest tenth:
\[
\approx 9.5\%
\]

Thus, the probability that Susan's first two pieces will be a fruit tart chew followed by a jelly treat is **9.5%**.

The correct answer is **D. 9.5%**.