To find the probability that Jameson gets a banana and Brittany gets a pear, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Since Jameson picks a fruit at random and does not replace it, after Jameson makes his selection, there will be one less fruit in the basket. Therefore, the total number of possible outcomes for Brittany's selection will be the number of remaining fruits in the basket.
Total number of favorable outcomes:
Jameson needs to select one out of the 2 bananas in the basket, so the number of possible outcomes favorable for Jameson is 2.
After Jameson's selection, Brittany needs to select one out of the 2 remaining pears in the basket, so the number of possible outcomes favorable for Brittany is 2.
So, the total number of favorable outcomes is 2 * 2 = 4.
To calculate the probability, you divide the number of favorable outcomes by the total number of possible outcomes:
Probability = favorable outcomes / total outcomes
= 4 / (total number of remaining fruits in the basket)
Now, let's determine the total number of remaining fruits in the basket. Initially, there were 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Since Jameson selected a banana, there is one less banana in the basket. Therefore, the remaining fruits in the basket are: 3 apples, 2 oranges, 1 banana, 2 pears, and 5 peaches.
The total number of remaining fruits in the basket is 3 + 2 + 1 + 2 + 5 = 13.
Now we can calculate the probability:
Probability = 4 / 13 ≈ 0.3077
So, the probability that Jameson gets a banana and Brittany gets a pear is approximately 0.3077 or 30.77%.