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Dependent Events Probability

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

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).

Read the lesson on dependent probability for more information and examples.

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

Work out the following.
When necessary, give your answer in fractions eg. 2/5

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:
a) both beads black.

b) both beads white.

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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