A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jack picks a fruit at random and does not replace it. Then Bethany picks a fruit at random. What is the probability that Jack gets a peach and Bethany gets an orange?
A. 10/27
B.5/91
C.5/98
D.93/182
Are you reading my other replies to your questions with the same concept?
ummm... hes anonymous. those probably werent his posts.
To find the probability that Jack gets a peach and Bethany gets an orange, we need to consider two independent events: Jack's choice and Bethany's choice.
Step 1: Calculate the probability of Jack getting a peach:
There are a total of 3 + 2 + 2 + 2 + 5 = 14 fruits in the basket. Out of these, there are 5 peaches.
Therefore, the probability of Jack getting a peach is 5/14.
Step 2: Calculate the probability of Bethany getting an orange:
After Jack has picked a fruit, there will be one less fruit in the basket. If Jack picked a peach, there will be 4 peaches left, while if Jack picked any other fruit, there will be 5 peaches left.
Out of the remaining fruits, there will be 2 oranges. So, the probability of Bethany getting an orange depends on Jack's choice:
- If Jack picks a peach: There will be 4 peaches and 13 fruits left, so the probability of Bethany getting an orange is 2/13 *Note: since Jack does not replace the fruit, the number of fruits in the basket changes with each pick.
- If Jack picks a fruit other than a peach: There will be 5 peaches and 13 fruits left, so the probability of Bethany getting an orange is still 2/13.
Step 3: Multiply the probabilities:
Since Jack's choice and Bethany's choice are independent events, we can multiply their probabilities to find the probability of both events happening:
Probability (Jack gets a peach and Bethany gets an orange) = Probability (Jack gets a peach) * Probability (Bethany gets an orange)
Probability (Jack gets a peach and Bethany gets an orange) = (5/14) * (2/13) = 10/182 = 5/91
Therefore, the correct answer is B. 5/91.