Jack is playing a game. when a player wins 3 consecutive games, the player receives 10 bonus points and then the player’s total score, s, increases by 5% of the player’s current points. jack currently has p points and has won 3 consecutive games. the function that represents a player’s points including the bonus points, b, is b(p) = . the function that gives the net points after the percentage increase in a player’s total points is s(p) = . jack’s total score after winning the bonus points, given by the function (s ∘ b)(p), is . nextreset

30

step-by-step explanation:

times by times

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