Question

A musician kept track of the concert arenas on this year's tour and found that 60% of the arenas were sold out. Of those that were not sold out, 25% had been on the previous tour schedule from last year, while 90% of those that were sold out were on the previous tour schedule. Which of the following represents the joint relative frequency of arenas that were sold out and not on the previous tour schedule?
75%
54%
30%
6%

Answer 1

Answer:

6%

Step-by-step explanation:

First, let's break this down:

60% of arenas sold out

• 90% had been on previous tour

Out of those arenas that did NOT sell out

• 25% had been on previous tour

We want to know the joint relative frequency of area that were sold out AND NOT on the previous tour schedule, therefore all the information about areas that did NOT sell out is irrelevant.

Because 90% of the areas that were sold out had been on the previous tour, 10% had NOT been on the previous tour.

Therefore, considering all the arenas, 10% of 60% of the arenas were sold out and not on the previous tour.

Let x equal the total number of arenas:

$(.10)(.60)x=0.06x$

Convert to percent

6%

Therefore, the joint relative frequency of sold out arenas that were not on the previous tour is 6%.