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Dependent Events

Dependent Events. Lesson 11-9 Pg. # 436-437. 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***:

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Dependent Events

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  1. Dependent Events Lesson 11-9 Pg. # 436-437

  2. 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.

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

  4. 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.

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

  6. 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.

  7. 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?

  8. 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.

  9. To find P (red, red), find the probability of each event and multiply. • Step 1.Find each probability. P (red:1st dart) = 4/8= 1/2 P (red:2nd 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.

  10. 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%.

  11. REPLACED: To find P (red, red), find the probability of each event and multiply. • Step 1.Find each probability. P (red:1st dart) = 4/8= 1/2 P (red:2nd 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.

  12. Example 4. • 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

  13. Example 5. • 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

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

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