The ratio of students who prefer coke to pepsi is 5 out of 7. if 84 students were surveyed, how many students prefer pepsi

If the ratio of students who prefer coke to Pepsi is 5 out of 7, it means that out of any total of surveyed students, 5/7 of the total prefers Pepsi, and 2/7 of the total doesn't.

So, out of 84 students, the number of those who prefer pepsi is

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