Question

read the story.
windy hills is in for a snowy month! meteorologists are predicting 2 snowstorms, each with a 75% chance of over 6 inches of snow. if it snows that much in a single storm,
sean knows hell get a snow day. how likely is it for sean to get a snow day both times?
sean simulates the situation by using a computer to randomly generate a pair of numbers
from 1 to 4. each time 1, 2, or 3 appears, it represents a snow day.
here are the results of 20 trials:
based on seans results, what is the probability that he will get a snow day both times?
%

Explanation:

Step1: Count favorable outcomes

Each pair of numbers represents two snow - storms. A snow - day occurs when the number is 1, 2, or 3. We need to count the number of pairs where both numbers are 1, 2, or 3.
Looking at the table:

• In the pair 23: both 2 and 3 (favorable)
• In the pair 14: 1 (first number favorable), 4 (second number not favorable)
• In the pair 23: both 2 and 3 (favorable)
• In the pair 34: 3 (first number favorable), 4 (second number not favorable)
• In the pair 42: 4 (first number not favorable), 2 (second number favorable)
• In the pair 24: 2 (first number favorable), 4 (second number not favorable)
• In the pair 13: both 1 and 3 (favorable)
• In the pair 24: 2 (first number favorable), 4 (second number not favorable)
• In the pair 14: 1 (first number favorable), 4 (second number not favorable)
• In the pair 23: both 2 and 3 (favorable)
• In the pair 14: 1 (first number favorable), 4 (second number not favorable)
• In the pair 31: 3 (first number favorable), 1 (second number favorable)
• In the pair 42: 4 (first number not favorable), 2 (second number favorable)
• In the pair 33: both 3 and 3 (favorable)
• In the pair 44: both 4 and 4 (not favorable)
• In the pair 43: 4 (first number not favorable), 3 (second number favorable)
• In the pair 41: 4 (first number not favorable), 1 (second number favorable)
• In the pair 32: 3 (first number favorable), 2 (second number favorable)
• In the pair 24: 2 (first number favorable), 4 (second number not favorable)
• In the pair 31: 3 (first number favorable), 1 (second number favorable)

The favorable pairs are 23, 23, 13, 23, 31, 33, 32, 31. The number of favorable pairs \(n = 8\).

Step2: Calculate probability

The formula for experimental probability is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The total number of trials \(N = 20\).
So, \(P=\frac{8}{20}\)
Simplify \(\frac{8}{20}=\frac{8\div4}{20\div4}=\frac{2}{5}\)
Convert \(\frac{2}{5}\) to a percentage: \(\frac{2}{5}\times100\%=(2\times20)\% = 40\%\)

Answer:

40