The Problem of the Points. Two players engage in a game. They are equally matched, and the chances of winning a point are the same for each player. The first player to score 10 points wins the $100 stakes. The game is interrupted suddenly when Player A has 7 points and Player B has 5 points. How should the stakes be divided fairly

Player A receives $77.34375 of the sakes

Player B receives $22.65625 of the stakes

Step-by-step explanation:

Given that at the time the game was interrupted, we have;

The number of points player A  has = 7 points

The number of points player B has = 5 points

The amount the first player to score 10 points wins = $100

The number of points remaining for player A to win the game = 3

The number of points remaining for player B to win the game = 5

Therefore, the number of trials remaining for a winner to emerge = 3 + 5 - 1 = 7 trials

We take the probability that Player A wins a point as success

We find the likelihood of Plater A winning by using binomial theory as follows;

Therefore, given that the likelihood of Player A winning = 99/128

The stakes should be divided such that Player A gets 99/128 share of the stakes while Player B gets 1 - 99/128 = 29/128 share of the stakes

Therefore, Player A gets (99/128) × $100 = $77.34375

Player B gets (29/128) × $100 =  $22.65625

step-by-step explanation:

mean or average is 40.6

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,