Question

a musician kept track of the concert arenas on this years 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?

Explanation:

Step1: Find the percentage of non - sold - out arenas

The percentage of sold - out arenas is 60%, so the percentage of non - sold - out arenas is $100\%-60\% = 40\%$.

Step2: Determine the percentage of sold - out arenas not on the previous tour schedule

We know that 90% of sold - out arenas were on the previous tour schedule. So the percentage of sold - out arenas not on the previous tour schedule is $(1 - 0.9)\times60\%$.
$(1 - 0.9)\times60\%=0.1\times60\% = 6\%$.

Answer:

6%