Chapter 10 – Data Analysis and Probability 10.8 – Probability of Independent and Dependent Events

Independent Events – two events where the outcome of one event does not affect the outcome of the other event Pulling a marble out of a bag, putting it back, and pulling another Dependent Events – two events where the outcome of the first event does affect the outcome of the second event Pulling a marble out of a bag, keeping it, then pulling another

10.8 – Probability of Independent and Dependent Events Example 1 Tell whether the events are independent or dependent. Your teacher chooses students at random to put math problems on the board. She chooses you first, and then chooses Sam from the remaining students. You roll a die, it shows 4. You roll the die again and it shows 3. There are 10 winning tickets in a collection of 500 tickets. You select a ticket, put it aside, and select another ticket.

10.8 – Probability of Independent and Dependent Events Conditional Probability – For two dependent events A and B, the probability that B will occur given that A has occurred Written P(B/A)

10.8 – Probability of Independent and Dependent Events Example 2 Use the table showing the numbers of members in the House of Representatives and Senate in the 110 th US Congress in DemocratRepublicanIndependentOther House Senate49 11

10.8 – Probability of Independent and Dependent Events DemocratRepublicanIndependentOther House Senate49 11 What is the probability that a Congress member was a democrat? What is the probability that a Senate member was a Republican? What is the probability that a Democrat was a member of the House?

10.8 – Probability of Independent and Dependent Events Probability of Independent and Dependent Events Independent Events – If A and B are independent events, then the probability that both A and B occur is P(A and B) = P(A) · P(B) Dependent Events - If A and B are dependent events, then the probability that both A and B occur is P(A and B) = P(A) · P(B/A)

10.8 – Probability of Independent and Dependent Events Example 3 You randomly select 2 cards from a standard deck of 52 cards. What is the probability that the first card is a heart and the second if a club if: You replace the first card before selecting the second? You do not replace the first card?

10.8 – Probability of Independent and Dependent Events Example 4 Find the probability of drawing the given cards at random from a standard 52-card deck with replacement A club, then a spade An ace, then a queen A face card, then a 4 A jack, then another jack

10.8 – Probability of Independent and Dependent Events Example 5 Find the probability of drawing the given cards at random from a standard 52-card deck without replacement A club, then a spade An ace, then a queen A face card, then a 4 A jack, then another jack

10.8 – Probability of Independent and Dependent Events Three or more events You can expand the formulas for the probabilities of two independent or dependent events to find the probabilities of three or more independent or dependent events

10.8 – Probability of Independent and Dependent Events Example 4 Suppose your area has 8 different Internet Service Providers (ISPs) and you and 3 friends randomly select your own ISP. What is the probability that you all choose different ISPs?

10.8 – Probability of Independent and Dependent Events HOMEWORK 10.8 Practice A Worksheet