Question: A gumball machine requests 25 cents and, in return, sends a colorful gumball down a chute into your waiting hands. The gumballs in this machine come in white, red, yellow, blue, pink, green, and orange. The colors are not evenly distributed; 1/10 of the gumballs are white, 11/40 of the gumballs are orange, and each remaining color represents 1/8 of the gumballs.
(a) Let the random variable R = 1 when a red gumball arrives, R = 1/2 when a pink or orange gumball arrives, and R = 0 otherwise. (R measures the redness of a gumball.) Compute E[R].
(b) Let the random variable Y = 1 when a yellow gumball arrives, Y = 1/2 when a green or orange gumball arrives, and Y = 0 otherwise. (Y measures the yellowness of a gumball.) Compute E[Y].
(c) Compute the expected value of R+Y.