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Independent and Dependent Events

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Independent Events

• For independent events, the outcome of one event does not affect the other event.

• The probability of two independent events can be found by multiplying the probability of the first event by the probability of the second event.

P(A and B) = P(A) P(B)

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Dependent Events

• If the outcome of one event affects the outcome of another event, the compound events are called dependent events.

• If two events, A and B, are dependent, then the probability of both events occurring is the product of the probability of A and the probability of B after A occurs.

P(A and B) = P(A) P(B following A)

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Independent Event ExampleTwo number cubes, one red and one blue, are rolled. What is the probability that the outcome of the red number cube is even and he outcome of a blue number cube is 5?

P(red number cube is even)

P(blue number cube is a 5)

P(red number cube is even and blue number cube is a 5)

The probability of rolling the red number cube and getting an even number and the blue number cube and getting a 5 is

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Dependent Event ExampleThere are 6 black socks and 4 white socks in a drawer. If one sock is taken out without looking and then a second one is taken out, what is the probability that they both will be black?

P(first sock is black) =

P(second sock is black)=

P(two black socks)=

The probability of picking two black socks is

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Practice ProblemsA card is drawn from a deck of 10 cards numbered 1 through 10 and a number cube is rolled. Find the probability of each below.

1.P(10 and 3) 2. P(two even numbers)

3. P(two numbers less than 4)

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Practice ProblemsThere are 4 red, 6 green, and 5 yellow pencils in a jar. Once a pencil is selected, it is not replaced. Find the probability of each below.

4. P(red then yellow) 5. P(two green)

6. P(green then yellow) 7. P(red then green)