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.
-
Total pieces of candy:
- Mint sticks: 5
- Jelly treats: 3
- Fruit tart chews: 12
Total number of pieces = 5 + 3 + 12 = 20 pieces.
-
Probability of the first piece being a fruit tart chew:
- There are 12 fruit tart chews out of 20 total pieces. \[ P(\text{first = fruit tart}) = \frac{12}{20} = 0.6 \]
-
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. \[ P(\text{second = jelly treat | first = fruit tart}) = \frac{3}{19} \]
-
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%.