Jenna is looking at two different options for a new cell phone plan. plan a has a fee of $50 plus an additional fee of $0.05 per minute. with this plan, the first 500 minutes are free. plan b has a fee of $20 plus an additional fee of $0.06 per minute. with this plan, the first 200 minutes are free. after how many minutes would both options cost the same amount?

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560