The Reds and the Cubs are playing 3 games. In each game the probability that the Reds win is 0.54. The probability of the Reds winning is not affected by who has won any previous games.

(a) What is the expected value for the number of games the Reds will win? (Give your answer correct to two decimal places.)

(b) What is the expected value for the number of games the Cubs will win? (Give your answer correct to two decimal places.)

(a) 1.6197

(b) 1.3803

Step-by-step explanation:

(a) Let X denote the number of games the Reds win. If Reds win exactly one it means that in the other two games Reds lost i.e Cubs won. Now,  the probability of the Reds losing is determined by . So, if X wins exactly times, then we should multiply the probabilities associated with

Now,

(b) Let Y denote the number of games won by Cubs. Then by the similar logic as above,

Now

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph

the answer is 40.

proof: