To study the relationship between gender and preference for

To study the relationship between gender and preference for a particular sport, a random sample of 220 people was taken. The gender and favorite sport were recorded, the results are given below.

Find the number of those studied who are female or prefer Nascar.

Solution

let,
n(A) denotes number of females
n(B) denotes who prefer Nascar

here:
n(A) = 32 + 45 + 23 = 100
n(B) = 32 + 38 = 70
n(A^B) = 32

use formula:
n(AUB) = n(A) + n(B) - n(A^B)
     = 100 + 70 - 32
     = 138

Answer: 138