50 points

audrey is playing a popular quest-style game on her games console. it randomly generates whole numbers in
the range 3 to 8 each time she hits the play button. she cannot start her quest until the total of the scores is 7
or greater. give exact answers, in simplest fraction form, for this question.

(a) find the probability distribution of the number of times audrey hits play, given the variable x, required
to achieve this total.

(b) find the expected number of hits of play required.

(c) find the variance for the number of hits of play required. (if you cannot get the exact answer for this part
write the answer as a decimal correct to 3 decimal places.)