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# 11.7 Probabilities Involving And

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### 11.7 Probabilities Involving And

1. 1. 11.7 Events Involving AND; Conditional Probability<br />
2. 2. AND Probabilities with Independent Events<br />Two events are independent events if the occurrence of either of them has no effect on the probability of the other.<br />Example: Winning the lottery twice; getting three consecutive tails when tossing a coin 3 times; being struck (or almost struck) by a lightning twice.<br />
3. 3. AND Probabilities with Independent Events<br /> P (A and B) = P (A) x P (B)<br />
4. 4. Problem 1<br /> Find the probability that a married couple will have 3 baby girls in a row.<br />1/8<br />
5. 5. Problem # 2<br />To play the Powerball, a player needs to select five numbers from 1-59 and a Powerball number from 1-39. Find the probability of winning twice in a row.<br />2.62 x 10^-17<br />
6. 6. Probability of an Event Happening at least Once<br />P (event happening at least once) =<br /> 1 – P (event does not happen)<br />Or<br />1 – P (not)<br />
7. 7. Problem # 3 (Ex. 3 from text)<br />If the probability that South Florida will be hit by a hurricane in any single year is 5/19. What is the probability that<br />A. South FL will be hit by a hurricane in 3 consecutive years?<br />B. South FL will not be hit by a hurricane in the next ten years?<br />C. South FL will be hit by a hurricane at least once in the next 10 years? <br />A. 125/6859 = 0.018<br />B. 0.047<br />C. 0.953<br />
8. 8. Problem # 4<br />In a poker game, the probability of getting a full house (3 cards of one number and 2 cards of a second number) is 3744 / 2,598,960. <br />A. Find the probability of getting a full house 3 times in a row.<br />B. Find the probability of not getting a full house after 20 games.<br />C. Find the probability of getting a full house at least once in 20 games.<br />A. 2.99 x 10^-9<br />B. 0.97<br />C. 0.03<br />
9. 9. AND Probabilities with Dependent Events<br />Two events are dependent if the occurrence of one of them has an effect on the probability of the other.<br />Example: You are dealt two cards from a 52-deck of card. Find the probability of getting 2 Aces.<br />P (A and B) = P (A) x P (B given that A has occurred)<br />
10. 10. Problem # 5<br />There are 20 chocolates in a box and all are identically shaped. 5 are solid chocolate, 8 are filled with caramel, 4 are filled with peanuts and 3 are filled with coconut. Find the probability of getting<br />A. 2 filled with caramels in a row<br />B. Solid chocolate followed by one filled with peanut<br />A. 0.15<br />B. .05<br />
11. 11. Problem 6 (Ex. 5 from text)<br />Three people are randomly selected, one person at a time, from 5 freshmen, 2 sophomores and 4 juniors. Find the probability that the first 2 people selected are freshmen and the 3rd is a junior.<br />8/99<br />
12. 12. Conditional Probability<br />The probability of event B, assuming that the event A has already occurred, is called conditional probability of B, given A. The probability is denoted by<br /> P (B A)<br />
13. 13. Problem 7 (Ex 6 from text)<br />A letter is randomly selected from the letters of the English alphabet. Find the probability of selecting a vowel, given that the outcome is a letter that precedes h.<br />2/7<br />
14. 14. Problem 8 (Ex 7 from text)<br />The table on the left shows the differences in the political ideology per 100 males and 100 females in the 2000 US presidential election.Find the probability that the person <br />A. is liberal, given that the person is female<br />B. is male, given that the person is conservative<br />