A basket contains the following pieces of fruit: 10 apples, 7 oranges, and 8 bananas. Jameson picks a fruit at random and does not replace it. Then Brittany picks a fruit at random. What is the probability that Jameson gets a banana and Brittany gets an orange?
There are a total of 25 pieces of fruit in the basket.
The probability of Jameson picking a banana is 8/25, as there are 8 bananas out of 25 total fruits in the basket. Once Jameson picks a fruit, there are now 24 fruits left in the basket, including 7 oranges. Therefore, the probability of Brittany picking an orange after Jameson has picked a banana is 7/24.
To find the probability of both events happening (Jameson getting a banana AND Brittany getting an orange), we multiply the probabilities:
P(Jameson gets a banana AND Brittany gets an orange) = (8/25)*(7/24)
Simplifying this expression gives:
P(Jameson gets a banana AND Brittany gets an orange) = 7/75
Therefore, the probability that Jameson gets a banana and Brittany gets an orange is 7/75.
To find the probability that Jameson gets a banana and Brittany gets an orange, we need to consider the total number of fruits and the number of possible outcomes.
Total number of fruits = 10 apples + 7 oranges + 8 bananas = 25 fruits
For Jameson to pick a banana, he has a 8/25 probability.
After Jameson picks a fruit, there are now 9 bananas left.
For Brittany to pick an orange, she has a 7/24 probability.
Therefore, the probability that Jameson gets a banana and Brittany gets an orange is (8/25) * (7/24) = 56/600 = 7/75.