Probability of Dependent Events Section 10.3 What key words tell us it is a dependent event?

Vocabulary Dependent event - two events whose occurrence of one event DOES affect the likelihood that the other event will occur Examples: – A deck of cards – Drawling a marble, without replacing it, then drawling another marble – Your teacher chooses one student to lead a group, and then chooses another student to lead another group

Things to Know

Finding the Probability of Two Dependent Events Step 1: Find the probability of A = P(A) Step 2: Find the probability of B after A has occurred = P(B after A) Step 3: Multiply the probability of A by the probability of B after A has occurred = P(A) x P(B after A) Step 4 : Simplify your fraction

Example 1 Tell whether the events are independent or dependent. Explain. 1.You flip heads on one coin and tails on another coin. 2.Your teacher chooses one student to lead a group, and then chooses another student to lead another group. 3.You choose a marble from a bag and set it aside. Then you choose another marble from the bag. 4.You choose a marble from a bag, record its color, and place it back into the bag. Then you choose another marble from the bag.

Your Turn Tell whether the events are independent or dependent. Explain. 1.You choose a blue marble from a bag and set it aside. Then you choose a green marble from the bag. 2.You roll a 5 on a number cube and spin blue on a spinner.

Example 2 You have four $20 bills and three $10 bills. You randomly choose a bill from your wallet to pay for lunch. You need more money, so you choose another bill. What is the probability that you choose a $20 bill, then a $10 bill?

Your Turn You have four $20 bills and three $10 bills. You randomly choose a bill from your wallet to pay for lunch. You need more money, so you choose another bill. What is the probability that both bills are $20 bills? What is the probability that both bills are $10 bills?

Example 3 You are guessing at two questions on a multiple choice test. Each question has three choices: A, B, and C. 1.What is the probability that you guess the correct answers to both questions? 2.Suppose you can eliminate one of the choices for each question. How does this change the probability that your guesses are correct?

Your Turn You randomly choose two fish from the bowl. What is the probability that the first is gold and without replacing it, the second is red?

Assignment What type of events/situations tell us it is a dependent event? What type of events/situations tell us it is a independent event? 1 – Easy Breezy, I got this 2 – I could use a little more practice 3 – I’m totally lost Page #5-27 all, skip #25