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# Pre-Cal 40S Slides May 22, 2008

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Dependant and independent probabilities. Introduction to calculating probabilities involving "OR" and "AND".

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### Pre-Cal 40S Slides May 22, 2008

1. 1. Types of Probability Einstein Was Wrong why? because!
2. 2. A coin is ﬂipped twice. Draw a tree diagram of the sample space and list the probabilities of each outcome.
3. 3. A marble is drawn, not replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?
4. 4. A marble is drawn, replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?
5. 5. Independent Events Events in which the outcome of one event does not affect the outcome of the other event. Dependent and independent probabilities ... A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and then REPLACED back in the bag. A second marble is selected, what is the probability that it is blue?
6. 6. Dependent Events If the outcome of one event affects the outcome of another event, then the events are said to be dependent events. Dependent and independent probabilities ... A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and NOT REPLACED back in the bag. A second marble is selected, what is the probability that it is blue?
7. 7. Identify each of the following as experiments involving dependent in independent events. Drag and Drop Your Answer INDEPENDENT DEPENDENT (a) Toss a coin and roll a die six. INDEPENDENT (b) Draw 2 cards from a 52 card deck, without replacement. DEPENDENT (c) Draw 2 cards from a 52 card deck, with replacement. INDEPENDENT
8. 8. A coin is ﬂipped three times. Draw a tree diagram of the sample space and list the probabilities of each outcome.
9. 9. In a family of 3 children, with boys and girls equally likely to be born, what is the probability that exactly 2 kids are girls?
10. 10. Two marbles are drawn. If the 1st marble is blue it is discarded and replaced with a red. Similarly, if the 1st marble is red it is discarded and replaced with a blue one. What is the probability that the second marble is blue?
11. 11. Two marbles are drawn. If the 1st marble is blue it is discarded and replaced with a red. Similarly, if the 1st marble is red it is discarded and replaced with a blue one. What is the probability that the second marble is blue?
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