The U.S. Weather Service reports that in a certain northern city it rains 35 days and snows 40 days in the winter. However, it rains and snows on only 10 of those days. Based on this information, what is the probability that it will rain or snow in that city on a particular winter day? Assume that there are 90 days of winter.

Question

The U.S. Weather Service reports that in a certain northern city it rains 35 days and snows 40 days in the winter. However, it rains and snows on only 10 of those days. Based on this information, what is the probability that it will rain or snow in that city on a particular winter day? Assume that there are 90 days of winter.

Answer 1

To calculate the probability of rain or snow on a particular winter day in the city, we need to use the concept of probability. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In this case, we are given the following information:
- It rains 35 days in the winter.
- It snows 40 days in the winter.
- It rains and snows on only 10 of those days.
- There are 90 days of winter.

To calculate the probability of rain or snow on a particular winter day, we can use the principle of inclusion-exclusion. The principle states that the probability of the union of two or more events is equal to the sum of their individual probabilities, minus the probability of the intersection of those events.

Let's calculate it step by step:

1. Calculate the probability of rain alone:
Since it rains on 35 days out of 90, the probability of rain on a particular winter day is 35/90.

2. Calculate the probability of snow alone:
Since it snows on 40 days out of 90, the probability of snow on a particular winter day is 40/90.

3. Calculate the probability of both rain and snow:
It is given that rain and snow occur on only 10 days out of 90, hence the probability of both rain and snow on a particular winter day is 10/90.

4. Calculate the probability of rain or snow:
To get the probability of rain or snow on a particular winter day, we sum the probabilities of rain alone, snow alone, and subtract the probability of both rain and snow, as per the principle of inclusion-exclusion.

P(rain or snow) = P(rain) + P(snow) - P(rain and snow)
= 35/90 + 40/90 - 10/90
= 65/90
= 13/18

Therefore, the probability that it will rain or snow in that city on a particular winter day is 13/18.