Dependent Events Lesson 11-9 Pg. #

CA Content Standards Statistics, Data Analysis, and Probability 3.5*** I understand the difference between independent and dependent events. Statistics, Data Analysis, and Probability 3.1***: I represent all possible outcomes for compound events and express the theoretical probability of each outcome. Statistics, Data Analysis, and Probability 3.4: I understand that the probability of one event following another, in independent trials, is the product of the two probabilities.

Vocabulary: DEPENDENT EVENTS Two events in which the outcome of the second is affected by the outcome of the first.

Objective Find the probability of dependent events. Math Link: You know how to find the probability of independent events. Now you will learn how to find the probability of dependent events.

Example 1. Find each probability; imagine that you are spinning the spinner two times. P (red, purple) P (not red, purple) P (red, green)

Please note… We just rehearsed probabilities involving two events that do not influence one another; now we are going to focus on compound events (2 events) in which our actions during the first event influence the outcome of the second event.

Example 2. The school carnival has a dart game. You can win a prize by hitting 2 red balloons. What is the probability of hitting one red balloon on the first try AND one red balloon on the second try?

A Little Background… Throwing two darts is a compound event. A compound event is a combination of two or more simple events. The outcome of the first dart DOES influence the outcome of the second dart. The two spins are dependent events.

To find P (red, red), find the probability of each event and multiply. Step 1. Find each probability. P (red:1 st dart) = 4 / 8 = 1 / 2 P (red:2 nd dart) = 3 / 7 Step 2. Multiply. 1 / 2 x 3 / 7 = 3 / 14 The probability of winning a prize is 3 / 14, or 3 out of 14 tries.

Example 3. In example 2, are you more likely to hit two red balloons if the first balloon is replaced before your second throw or if it is not replaced? NOT REPLACED: From Example 2, we know that the probability of hitting two red balloons if the balloon is not replaced is 3 out of 14, or 21%.

REPLACED: To find P (red, red), find the probability of each event and multiply. Step 1. Find each probability. P (red:1 st dart) = 4 / 8 = 1 / 2 P (red:2 nd dart) = 4 / 8 = 1 / 2 Step 2. Multiply. 1 / 2 x 1 / 2 = 1 / 4 The probability of winning a prize is 1 / 4, or 25%, if the balloon is replaced. Therefore, we have a greater chance of winning if the balloon is replaced before the second dart.

The letters of the word MATHEMATICS were placed in a bag; find the probability of forming the word AT if the first letter is put back before picking the second letter. Step 1. Find each probability. P (A) = 2 / 11 P (T) = 2 / 11 Step 2. Multiply. 2 / 11 x 2 / 11 = 4 / 121 Example 4.

The letters of the word MATHEMATICS were placed in a bag; find the P (H, C) if the first letter is NOT put back before picking the second letter. Step 1. Find each probability. P (H- First draw)= 1 / 11 P (C- Second draw)= 1 / 10 Step 2. Multiply. 1 / 11 x 1 / 10 = 1 / 110 Example 5.

Moral of the Story For dependent events, the outcome of the first event affects the outcome of the second event.