Practice Sheet 8 – 6
For questions 1 – 3, tell whether the events are independent or dependent.
1. A teacher is randomly assigning you, your friend, and 4 other students to 6 different
seats.
Event A: You are assigned the first seat.
Event B: Your friend is assigned the second seat.
2. A computer randomly chooses a digit from 1 to 100. A digit can be chosen more than
once.
Event A: The digit is prime.
Event B: The digit is odd.
3. You randomly choose a utensil from a drawer with 12 spoons, 8 forks, and 6 knives.
Without replacing the first item, you draw another.
Event A: You draw a spoon first.
Event B: You draw a fork second.
Solve each problem below:
4. A gumball machine has 21 red gumballs, 24 yellow gumballs, and 15 blue gumballs. The
gumballs are randomly mixed.
a. What is the probability that the gumball machine dispenses 2 red gumballs in a
row?
b. What is the probability that the gumball machine dispenses a red gumball, then
a yellow gumball?
c. What is the probability that the gumball machine dispenses a red gumball, then
a blue gumball?
5. A package of daisy seeds claims that the probability that each seed in the package
sprouts under optimal conditions is 55%. Suppose you plant two daisy seeds under
optimal conditions.
a. What is the probability that both seeds sprout?
b. What is the probability that neither of the seeds sprouts?
6. A drawer contains 4 blue socks, 6 gray socks, and 8 black socks. You randomly choose
one sock, then another from the drawer.
a. Find the probability that you choose 2 blue socks.
b. Find the probability that you choose 2 gray socks.
c. Find the probability that you choose 2 black socks.
d. Find the probability that you choose 2 socks that match.
7. A bag contains 20 red marbles and 20 blue marbles. You randomly draw a marble from
the bag, and then randomly draw another marble. Do you have a greater probability of
drawing 2 red marbles if you replace the first marble after you draw it, or if you do not
replace the first marble? Explain.