Testing for Independent Events Practice Worksheet

You flip a fair coin and roll a fair six-sided die. What is the probability of getting heads and rolling a 5?

1/12. P(Heads) = 1/2 and P(5) = 1/6. Since coin flips and die rolls are independent, P(Heads and 5) = (1/2) * (1/6) = 1/12.

Events A and B are independent. P(A) = 0.4 and P(B) = 0.35. Find P(A and B).

0.14. For independent events, P(A and B) = 0.4 * 0.35 = 0.14.

A card is drawn from a standard 52-card deck. Event A is drawing a King. Event B is drawing a Heart. Are events A and B independent? Show your work.

Yes. P(King) = 4/52 = 1/13. P(Heart) = 13/52 = 1/4. Their product is (1/13) * (1/4) = 1/52. The intersection is the King of Hearts, which has probability 1/52. Because the product equals the intersection, they are independent.

A jar contains 3 red marbles and 2 blue marbles. You draw two marbles without replacement. Event A is the first marble is red. Event B is the second marble is red. Are A and B independent?

No, they are dependent. P(A) = 3/5 and P(B) = 3/5, giving a product of 9/25 = 0.36. P(A and B) = (3/5) * (2/4) = 6/20 = 0.30. Since 0.36 does not equal 0.30, the events are dependent.

Events C and D have probabilities P(C) = 0.6, P(D) = 0.5, and P(C and D) = 0.28. Are events C and D independent?

No. P(C) * P(D) = 0.6 * 0.5 = 0.30. Since P(C and D) = 0.28, which is not equal to 0.30, C and D are dependent.

Two events, E and F, are mutually exclusive (disjoint), and both have probability 0.2. Can events E and F be independent?

No. Because they are mutually exclusive, P(E and F) = 0. However, P(E) * P(F) = 0.2 * 0.2 = 0.04. Since 0 does not equal 0.04, disjoint events with positive probabilities are never independent.