Solve. Show your work. 7.
A spinner is equally divided into three equal sectors and marked 2, 3, and 5. Five number cards are labeled 1, 1, 2, 3, and 4. Mike spins the spinner and draws a card randomly.
a) Use a possibility diagram to find the probability that Mike gets a zero when he subtracts the number on the spinner from the number on the card.
b)
Use a possibility diagram to find the probability that the product of the two resulting numbers is odd.
c)
What is the probability that the product of the two resulting numbers is at least 12.

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 0.7, find the probability that Steven will go to the gym on each of the 2 consecutive days.
d) If x 0.58, find the probability that Steven will not go to the gym on each of the 2 consecutive days.
e) If x 0.2, find the probability that Steven will go to the gym on at most one of the two consecutive days.