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Independent and Dependent Events

Independent and Dependent Events. 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.

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Independent and Dependent Events

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  1. Independent and Dependent Events

  2. 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)

  3. 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)

  4. Independent Event Example Two 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

  5. Dependent Event Example There 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

  6. Practice Problems A 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. • P(10 and 3) 2. P(two even numbers) 3. P(two numbers less than 4)

  7. Practice Problems There 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)

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