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?
To find the probability of Jonas getting a peach and Beth getting an apple, we need to first know the total number of fruit in the basket. Adding up the number of apples, oranges, bananas, pears, and peaches, we get:
3 (apples) + 2 (oranges) + 2 (bananas) + 2 (pears) + 5 (peaches) = 14 (total fruit)
Since Jonas picks a fruit at random and does not replace it, there are now 13 pieces of fruit left in the basket. However, since we are only interested in the probability Jonas gets a peach and Beth gets an apple, we only need to consider those two fruits.
The number of peaches is 5, and the number of apples is 3. Therefore, the probability of Jonas picking a peach is 5/13, and if Jonas picks a peach, there will be only 2 apples left out of 12 remaining fruits. Thus, the probability of Beth picking an apple is 2/12.
To find the probability of both events occurring, we multiply the two probabilities together:
(5/13) * (2/12) = 10/156
So, the probability that Jonas gets a peach and Beth gets an apple is 10/156.
To calculate the probability that Jonas gets a peach and Beth gets an apple, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of fruits in the basket = 3 apples + 2 oranges + 2 bananas + 2 pears + 5 peaches = 14 fruits
When Jonas randomly picks a fruit, the total number of possible outcomes is decreased by one. So, there are 13 fruits remaining in the basket.
The number of favorable outcomes for Jonas to pick a peach is 5 since there are 5 peaches in the basket.
After Jonas picks a peach, Beth will randomly pick from the remaining fruits. The total number of possible outcomes for Beth is 13 fruits since one fruit has been removed.
The number of favorable outcomes for Beth to pick an apple is 3 since there are 3 apples remaining in the basket.
Therefore, the probability that Jonas gets a peach and Beth gets an apple can be calculated as:
Probability = (Number of favorable outcomes)/(Total number of possible outcomes)
= (5 peaches / 14 fruits) * (3 apples / 13 fruits)
= 15/182 ≈ 0.0824
So, the probability that Jonas gets a peach and Beth gets an apple is approximately 0.0824 or 8.24%.