Question

Heavy Snowfall (H) 0.95 (Lines going to both Closed and Open). Light snowfall (L) 0.90 (Lines going both to Closed and Open). H (Heavy snowfall). L (Light snowfall). C (Closed). O (Open). 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 65% chance for heavy snow.

0.90 (Light snow and Open)
0.95 (Heavy snow and Closed)

Answer 1

To find the probability that the school is closed tomorrow given that there is a 65% chance for heavy snow, we can use the law of total probability.

We have the following probabilities based on the weather conditions:

- Probability of heavy snow (H) = 0.65
- Probability of light snow (L) = 1 - 0.65 = 0.35

From the problem, we know:

- Probability of school being closed given heavy snow (C|H) = 0.95
- Probability of school being closed given light snow (C|L) = 1 - 0.90 = 0.10 (since the probability of being open is 0.90)

Now we can calculate the total probability of the school being closed (C):

\[
P(C) = P(C|H) \cdot P(H) + P(C|L) \cdot P(L)
\]

Substituting the values we have:

\[
P(C) = (0.95 \cdot 0.65) + (0.10 \cdot 0.35)
\]

Calculating each term:

1. \( 0.95 \cdot 0.65 = 0.6175 \)
2. \( 0.10 \cdot 0.35 = 0.035 \)

Now sum these results:

\[
P(C) = 0.6175 + 0.035 = 0.6525
\]

To express this probability as a percent, we multiply by 100:

\[
P(C) = 0.6525 \times 100 = 65.25\%
\]

Thus, the probability that the school is closed tomorrow is **65.25%**.