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 that it will rain or snow on a particular winter day in the city, we can use the principle of inclusion-exclusion.

Let's denote:
- R: the event that it rains on a particular winter day.
- S: the event that it snows on a particular winter day.
- A: the event that it either rains or snows on a particular winter day.

We are given that it rains on 35 days, snows on 40 days, and both rains and snows on 10 days.

To find the probability of A, we can use the formula:

P(A) = P(R) + P(S) - P(R and S)

P(R) = 35/90 (since it rains on 35 out of 90 days)
P(S) = 40/90 (since it snows on 40 out of 90 days)
P(R and S) = 10/90 (since it rains and snows on 10 out of 90 days)

Substituting the values into the formula:

P(A) = (35/90) + (40/90) - (10/90)
P(A) = 75/90
P(A) = 5/6

Therefore, the probability that it will rain or snow on a particular winter day in the city is 5/6 or approximately 0.8333.

Answer 2

To calculate the probability that it will rain or snow on a particular winter day in the northern city, you need to consider the total number of days it rains and snows (which is 10) out of the total number of days in winter (90).

The probability can be calculated using the formula:

Probability = Number of Successful Outcomes / Total Number of Possible Outcomes

In this case, the successful outcomes are the days when it rains or snows, which is 10. The total possible outcomes are the total number of winter days, which is 90.

Therefore, the probability that it will rain or snow on a particular winter day in that northern city is:

Probability = 10 / 90

Simplifying the fraction, we get:

Probability = 1 / 9

So, the probability that it will rain or snow on a particular winter day is 1/9 or approximately 0.1111 (rounded to four decimal places).

Answer 3

P(A) + P(B) - P(A and B)

35/90 + 40/90 -10/90 = 13/18