Question
Question
Alicia has a bowl of fruit on her kitchen table. On Monday, the bowl of fruit contains 5
bananas,
2 tangerines, and
3 pears. She will select a piece of fruit for her lunch at random each morning. What is the probability she will not choose a pear on Monday or Tuesday?
Responses
Answers
Answered by
GPT-4o mini
To find the probability that Alicia will not choose a pear on Monday or Tuesday, we first need to determine the total amounts and probabilities for each day.
On Monday, the bowl contains:
- 5 bananas
- 2 tangerines
- 3 pears
Total pieces of fruit = 5 + 2 + 3 = 10.
The probability of not choosing a pear on Monday is the number of fruits that are not pears divided by the total number of fruits:
- Fruits that are not pears = 5 (bananas) + 2 (tangerines) = 7.
So, the probability of not choosing a pear on Monday (P(NP-Monday)) is:
\[
P(NP-Monday) = \frac{7}{10}
\]
On Tuesday, the bowl contains the same fruits as on Monday because no fruit has been removed yet. Therefore, the probability of not choosing a pear on Tuesday (P(NP-Tuesday)) is also:
\[
P(NP-Tuesday) = \frac{7}{10}
\]
Since the choices on Monday and Tuesday are independent events, we can find the overall probability of not choosing a pear on both days by multiplying the probabilities together:
\[
P(NP-Monday \text{ and } NP-Tuesday) = P(NP-Monday) \times P(NP-Tuesday) = \frac{7}{10} \times \frac{7}{10} = \frac{49}{100}
\]
Thus, the probability that Alicia will not choose a pear on either Monday or Tuesday is \(\frac{49}{100}\) or 0.49.
On Monday, the bowl contains:
- 5 bananas
- 2 tangerines
- 3 pears
Total pieces of fruit = 5 + 2 + 3 = 10.
The probability of not choosing a pear on Monday is the number of fruits that are not pears divided by the total number of fruits:
- Fruits that are not pears = 5 (bananas) + 2 (tangerines) = 7.
So, the probability of not choosing a pear on Monday (P(NP-Monday)) is:
\[
P(NP-Monday) = \frac{7}{10}
\]
On Tuesday, the bowl contains the same fruits as on Monday because no fruit has been removed yet. Therefore, the probability of not choosing a pear on Tuesday (P(NP-Tuesday)) is also:
\[
P(NP-Tuesday) = \frac{7}{10}
\]
Since the choices on Monday and Tuesday are independent events, we can find the overall probability of not choosing a pear on both days by multiplying the probabilities together:
\[
P(NP-Monday \text{ and } NP-Tuesday) = P(NP-Monday) \times P(NP-Tuesday) = \frac{7}{10} \times \frac{7}{10} = \frac{49}{100}
\]
Thus, the probability that Alicia will not choose a pear on either Monday or Tuesday is \(\frac{49}{100}\) or 0.49.