9. Suppose that in a community of 4000 adults, 300 bike or swim or do both, 160 swim,
and 120 swim and bike. What is the probability that an adult, selected at random
from this community, bikes? [HINT: Use $P(A \cup B) = P(A) + P(B) - P(A \cap B)$]
10. In Ohio's Pick 4 game, you pay $1 to select a sequence of four digits, such as 7709. If
you buy only one ticket and win, your prize is $5000 and your net gain is $4999.
(a) If you buy one ticket, what is the probability of winning?
(b) Construct a table describing the probability distribution corresponding to the
purchase of one Pick 4 ticket.
(c) If you play this game once every day, find the mean number of wins in a year that
has 365 days.
(d) What is the expected value for the purchase of one ticket?
11. Suppose that 40% of the adults get enough sleep and 46% exercise regularly. Assume
that 24% do both. What is the probability that an adult gets enough sleep OR exercises
regularly? [HINT: Venn Diagram followed by a rule]