A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jonas picks a fruit at random and does not replace it. Then Beth picks a fruit at random. What is the probability that Jonas gets a peach and Beth gets an apple?
A. 15/182
B. 8/27
C. 4/91
D. 15/196
its 15/182
14 total fruits, so
5/14 * 3/13 = ____
To find the probability that Jonas gets a peach and Beth gets an apple, we need to calculate the individual probabilities and multiply them together.
Step 1: Calculate the probability that Jonas gets a peach.
- There are 14 fruits in total.
- There are 5 peaches.
- Therefore, the probability that Jonas gets a peach is 5/14.
Step 2: Calculate the probability that Beth gets an apple.
- After Jonas picks a fruit, there are 13 fruits left.
- There are 3 apples.
- Therefore, the probability that Beth gets an apple is 3/13.
Step 3: Multiply the probabilities together.
- The probability that Jonas gets a peach and Beth gets an apple is (5/14) * (3/13).
- This equals 15/182.
Therefore, the correct answer is A. 15/182.
To find the probability that Jonas gets a peach and Beth gets an apple, we first need to determine the total number of fruit in the basket. In this case, there are 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches, for a total of 3 + 2 + 2 + 2 + 5 = 14 fruit.
For Jonas to get a peach, there are 5 peaches out of the 14 total fruits, so the probability that Jonas gets a peach is 5/14.
After Jonas has picked a fruit and not replaced it, there are now 13 fruit left in the basket. To calculate the probability that Beth gets an apple, we need to consider that there are 2 apples left. Therefore, the probability that she gets an apple is 2/13.
To find the probability that both events occur (Jonas gets a peach and Beth gets an apple), we multiply the individual probabilities together: (5/14) * (2/13) = 10/182.
The answer is not listed in the given options, but upon simplification, 10/182 can be reduced to 5/91.
Thus, the correct answer is C. 5/91.