Mary has scored 99, 83, 74, and 69 on her previous four tests. What score does she need on her next test so that her average (mean) is 77?

66

Step-by-step explanation:

mean = the sum of the value / the number of the value

when we calculate the some must be 385 so the sum of the given value gives 319 so to reach the average 77 she must score 66

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