Question

In the last several weeks, 67 days saw rain and 23 days saw high winds. In that same time period, 13 days saw both rain and high winds. How many days saw either rain or high winds

Answer 1

The number of days that had either rain or high winds for the considered case is 77

What is the addition rule of size for two subsets?

For two subsets A and B of the universal set U, we have:

$n(A \cup B) = n(A) + n(B) - n(A \cap B)$

Assume that:

A and B be the subsets of what happens on each day.

Then in the days of last several weeks , we take:

• A = set of days which had rain
• B = set of days which had high winds,

then, as per the data given, we get:

• n(A) = number of days seeing rain = 67
• n(B) = number of days seeing high winds = 23
• n(A ∩B) = number of days seeing both rain and high winds = 13

Thus, we get:

$n(A \cup B) = n(A) + n(B) - n(A \cap B)\\n(A \cup B) = 67 + 23 - 13 = 77$

Thus, n(A ∪B) = number of days seeing either rain or high winds = 77

Thus, the number of days that had either rain or high winds for the considered case is 77

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