Ineed with these two problems. need an explanation, steps, and an answer.

Let be the scores of the first 8 quizzes. We know that the average of these scores is 85, so we have

The average of the first 9 scores is 81, and it is given by

But we know that the sum of the first 8 is 680:

And we can solve for the nineth score: multiply both sides by 9:

Subtract 680 from both sides:

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