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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".

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

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Statistics
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### Transcript

• 1. Types of Probability Einstein Was Wrong why? because!
• 2. A coin is ﬂipped twice. Draw a tree diagram of the sample space and list the probabilities of each outcome.
• 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. 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. 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. 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. 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. A coin is ﬂipped three times. Draw a tree diagram of the sample space and list the probabilities of each outcome.
• 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. 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. 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?