Question

The tree diagram relates the weather forecast and school closings. Find the probability ( as a percent) that the school is closed tomorrow if there is a 60 % chance of heavy snow. H= heavy snowfall, l= light snowfall, c= closed, and o= open.

H to c is 0.95
H to 0 is 0.05
L to o is 0.90
L to c is 0.10

Answer 1

To find the probability that the school is closed tomorrow, we can use the Law of Total Probability by considering the two scenarios: heavy snowfall (H) and light snowfall (L).

### Given probabilities:
- Probability of heavy snow: \( P(H) = 0.60 \)
- Probability of light snow: \( P(L) = 1 - P(H) = 0.40 \)

From the tree diagram:
- Probability of school closed given heavy snow: \( P(C | H) = 0.95 \)
- Probability of school open given heavy snow: \( P(O | H) = 0.05 \)
- Probability of school open given light snow: \( P(O | L) = 0.90 \)
- Probability of school closed given light snow: \( P(C | L) = 0.10 \)

### To calculate:

1. **Probability of closing school due to heavy snowfall:**
\[
P(C \cap H) = P(H) \times P(C | H) = 0.60 \times 0.95 = 0.57
\]

2. **Probability of closing school due to light snowfall:**
\[
P(C \cap L) = P(L) \times P(C | L) = 0.40 \times 0.10 = 0.04
\]

3. **Total probability that the school is closed:**
\[
P(C) = P(C \cap H) + P(C \cap L) = 0.57 + 0.04 = 0.61
\]

4. **Convert the probability to a percentage:**
\[
P(C) = 0.61 \times 100 = 61\%
\]

### Conclusion:
The probability that the school is closed tomorrow is **61%**.