Download 11.3 Independent and Dependent Events

11.3 Independent and Dependent Events
Independent Events ­ 2 or more events where the occurrence of one does NOT affect the other. Probability of Independent Events
P(A and B) = P(A) P(B)
Ex: You toss a coin and roll a dice. What is the probability you get heads and a 6? Dependent Events ­ 2 or more events where the occurrence of one event affects the probability (and sample space!) of the other. Probability of Dependent Events
P(A and B) = P(A) P(B/A) where P(B/A) is the probability of B, given that A has occured. Ex: What is the probability that you roll 2 die and the first one is a 3, and their sum is 8? Ex: Two cards are drawn from a deck of 52. Determine if Independent or Dependent. Then, find the probability ...
Ex: Selecting a king and then a 7 when the first card is replaced. Ex: Selecting a face card and then a heart when the first card is not replaced.
Homework Page 815 (1­13, 17­22))
11.3 YOU DO!
Two number cubes are rolled ­ one blue and one yellow. Determine if Independant or Dependent. Then, find the probability ...
Independent Independent
OR
Dependent 1) The blue cube is a 4 and the yellow cube is odd number.
2) The blue cube shows a 2 and the sum is 7. 3) The yellow cube shows a multiple of 3 and the product is 6. 6) selecting two face cards when the first card
Two cards are drawn from a deck of 52. Determine if Independent or Dependent. Then, find the
5) selecting a king and then a spade when
first card is not replaced.
4) selecting two kings when the first card it repla
Homework Page 815
1­23, 32­33
1. Vocabulary Two events are _______________if the occurrence of one event does not affect the probability of the other event.
independent or dependent Find each probability. 2. rolling a 1 and then another 1 when a number cube is rolled twice. 3. a coin landing heads up on every toss when it is tossed 3 times. Two number cubes are rolled ­ one blue and one yellow. Explain why the events are dependent. Then find the indicated probability. 4. The blue cube shows a 4 and the product is less than 20. 5. The yellow cube shows a multiple of 3, given that the product is 6. A bag contains 20 checkers ­ 10 red and 10 black. Determine whether the events are independent or dependent. Find the indicated probability.
8. selecting 2 black checkers when they are chosen at random with replacement.
9. selecting 2 black checkers when they are chosen at random without replacement.
273 high school students were chosen at random in 1982 and contacted again in 1992. Each person was classified according to highest level of education completed and family income while in high school. The results are given in the table.
Find the probabilities below.
Change??
1) that a student is a high school graduate is from a low income family
2) that a student selected is from a low income family and is a college graduate