Question

# The probability of rain in San Francisco on a given day is 1/6. The probability of rain in Miami is 5/6. Use two number cubes to find the simulated probability of rain in both cities.

Probability and combinatorics
The probability of rain in San Francisco on a given day is $$\displaystyle\frac{{1}}{{6}}$$. The probability of rain in Miami is $$\displaystyle\frac{{5}}{{6}}$$. Use two number cubes to find the simulated probability of rain in both cities.

2020-10-24
Given:
Probability rain San Francisco= $$\displaystyle\frac{{1}}{{6}}$$
Probability rain Miami = $$\displaystyle\frac{{5}}{{6}}$$
Let us consider a blue and red number cube. The blue number cube will represent San Francisco and the red number cube will represent Miami.
A number cube has 6 possible outcomes: 1, 2, 3, 4, 5,6.
The probability of rain in San Franciscois then simulated by the blue number cube, when exactly 1 of the 6 possible outcomes on the blue number cube correspond with rain (while the other outcomes correspond with no rain) as the probability of rain needs to be 1/6.
Let Blue 1=rain in San Francisco and Blue 2, 3, 4, 5, 6=no rain in San Francisco.
The probability of rain in Miami is then simulated by the red number cube, when exactly 5 of the 6 possible outcomes on the red number cuthe correspond with rain (while the other outcome corresponds with no rain) as the probability of rain needs to be 5/6.
Tet Red 1=no rain it Miami and Red 2, 3, 4, 5, 6 = rain in Miami