Question
7 On any day the probability that it rains is \( \frac{1}{3} \). When it rains the probability that Amira goes fishing is \( \frac{3}{5} \) When it does not rain the probability that Amira goes fishing is \( \frac{3}{4} \). (a) In a period of 60 days on how many days is it expected to rain?
Ask by Gray Mitchell. in Kenya
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
It is expected to rain on 20 days out of 60.
Solution
To determine the expected number of days it will rain over a 60-day period, we use the concept of **expected value** in probability.
**Given:**
- Probability of raining on any given day, \( P(\text{Rain}) = \frac{1}{3} \).
**Calculation:**
- **Expected number of rainy days** = Total number of days × Probability of rain on any given day.
\[
\text{Expected rainy days} = 60 \times \frac{1}{3} = 20
\]
**Answer:**
(a) It is expected to rain on 20 days out of the 60-day period.
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Simplify this solution The Deep Dive
In a 60-day period, the expected number of days it rains can be calculated using the probability of rain. Since the probability that it rains on any given day is \( \frac{1}{3} \), you can multiply this probability by the number of days: \[ \text{Expected days of rain} = \text{Total days} \times \text{Probability of rain} = 60 \times \frac{1}{3} = 20 \] So, it is expected to rain on 20 days within a 60-day period.
