Question

A survey is taken of 86 people who vacationed at a dude ranch. The following information was obtained..."

What is the number of people who took horseback riding lessons, attended the barn dance, and bought souvenirs?

a) 13

b) 27

c) 62

d) 21

Answer 1

To find the number of people who took horseback riding lessons, attended the barn dance, and bought souvenirs, we can use the formula for finding the intersection of three events.

Step-by-step explanation:

To find the number of people who took horseback riding lessons, attended the barn dance, and bought souvenirs, we need to find the intersection of these three events. Let's assign variables to each event:

• A = people who took horseback riding lessons
• B = people who attended the barn dance
• C = people who bought souvenirs

From the given information, we know that:

• n(A) = 13
• n(B) = 27
• n(C) = 62
• n(U) = 86 (total number of people surveyed)

To find the number of people who took horseback riding lessons, attended the barn dance, and bought souvenirs, we can use the formula:

n(A ∩ B ∩ C) = n(A) + n(B) + n(C) - 2(n(A ∩ B) + n(A ∩ C) + n(B ∩ C)) + n(A ∩ B ∩ C)

Substituting the given values into the formula, we get:

n(A ∩ B ∩ C) = 13 + 27 + 62 - 2(0) + n(A ∩ B ∩ C)

Simplifying the equation, we have:

n(A ∩ B ∩ C) = 102

Therefore, the number of people who took horseback riding lessons, attended the barn dance, and bought souvenirs is 102.