Math probability questions ( need help answering question)

Question

8. The probability of Steven going to the gym is x. The events of Steven going and not going to the gym are mutually exclusive and complementary.

a) Write an expression to represent the probability that Steven will not go to the gym.

b) Draw a tree diagram to represent the possible outcomes for two Consecutive days.

c) If x 5 0.7, find the probability that Steven will go to the gym on each of the two consecutive days.

d) If x 5 0.58, find the probability that Steven will not go to the gym on each of the two consecutive days.

e) If x 5 0.2, find the probability that Steven will go to the gym on at most one of the two consecutive days.

Answer 1

if Pr(g) = x

then Pr(not g) = 1-x

if g and not g are mutually exclusive and complementary

with g and not g exhausting all possibilities.

Pr(g or not g) = 1, a certainty

Pr (g and not g) = 0, an impossibility