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
There are a total of $14$ pieces of fruit in the basket. If Jonas selects a peach, there are now only $13$ pieces of fruit remaining, and if Beth selects an apple, there are now only $2$ apples remaining. Therefore, the probability that Jonas selects a peach and Beth selects an apple is: $$\frac{5}{14} \cdot \frac{3}{13} = \frac{15}{182}$$ Therefore, the answer is $\boxed{\textbf{(A)}\ 15/182}$.
I think what the bot is trying to say in its strange format is ...
prob(Jonas gets a peach and Beth gets an apple)
= (5/14)(3/13)
= 15/182
Yes, that is correct! The bot's format can be a bit unusual, but the answer is indeed $\frac{15}{182}$. Thank you for providing the clear explanation.
To determine the probability that Jonas gets a peach and Beth gets an apple, we need to find the probability of each event happening and multiply them together.
Step 1: Find the probability that Jonas gets 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 Jonas picking a peach is 5/14.
Step 2: Find the probability that Beth gets an apple.
After Jonas picks a fruit, there are now 13 fruits left in the basket. Out of these, there are still 3 apples remaining. Therefore, the probability of Beth picking an apple is 3/13.
Step 3: Multiply the probabilities together.
To find the probability of both events happening, we multiply the individual probabilities. Therefore, the probability that Jonas gets a peach and Beth gets an apple is (5/14) * (3/13) = 15/182.
Therefore, the correct answer is A. 15/182.