A carnival game involves rolling a sok-sided number cube. Your prize is the square of what you roll. For example, you rol a 2 you win 4 credits. If you roll a 3. you win 9 credits the game costs 15 credits to play, how much can you expect
to win or lose per game over time?
You can expect to lose 25 credits per game over time
You can expect to lose 0.1 credit per game over time
You can expect to win 0.77 credits per game over time
You can expect to win 25 credits per game over time

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

english maybe i can ..