 # Dependent Events Probability Worksheets

Objective: I know how to find the probability events that are dependent.

What are dependent events?

Events are dependent if the outcome of one event affects the outcome of another. For example, if you draw two colored balls from a bag and the first ball is not replaced before you draw the second ball then the outcome of the second draw will be affected by the outcome of the first draw.

If A and B are dependent events, then the probability of A happening AND the probability of B happening, given A, is P(A) × P(B after A).

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Work out the following.

1. A bag contains 9 blue marbles and 3 red marbles. Two marbles are drawn at random.
What is the probability of getting:
a) two red marbles?

b) one red marble and one blue marble?

c) two blue marbles?

2. A bag contains 15 beads. Six are black and the rest are white. Two beads are drawn at random.
Find the probability of getting:

c) at least one white bead.

3. In a pack of 52 cards, 4 of the cards are Kings. Two cards are randomly picked from the pack.
Find the probability of picking:
a) two Kings

b) at least one King

c) not a King

4. Twelve people work together: four of them are managers and eight of them are office workers. Two people are chosen at random from the twelve members of the group. Calculate the probability that one is a manager and one is an office worker. Express your answer as a fraction.

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