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Probability Practice

Probability Practice. Chapter 10. Example 1:. A coin is tossed three times and the results are recorded. What is the probability of getting exactly two heads? At least two heads? No heads?. Example 1 answers. P(exactly 2H) = 3/8 P(at least 2H) = ½ P (H’)=1/8. Example 2.

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Probability Practice

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  1. Probability Practice Chapter 10

  2. Example 1: • A coin is tossed three times and the results are recorded. What is the probability of getting exactly two heads? At least two heads? No heads?

  3. Example 1 answers • P(exactly 2H) = 3/8 • P(at least 2H) = ½ • P (H’)=1/8

  4. Example 2 • A five-card poker hand is drawn from a standard deck of 52 cards. What is the probability that all five cards are spades?

  5. Example 2 answer

  6. Example 3 • A bag contains 20 tennis balls, of which four are defective. If two tennis balls are selected at random from the bag, what is the probability that both are defective?

  7. Example 3 answer or

  8. Example 4 • A jug contains 10 red marbles and 15 blue marbles. Six marbles are drawn at random from the jug. What is the probability that at least one marble is red?

  9. 2 ways to solve (count or use complement) • COUNT: • COMPLEMENT: (count not RED aka BLUE)

  10. Example 5 • A card is drawn at random from a standard deck of 52 cards. What is the probability that the card is either a seven or a face card?

  11. Example 5 • The events are mutually exclusive so you can just add the probabilities:

  12. Example 6 • What is the probability that a card drawn at random from a standard 52-card deck is either an ace or aheart?

  13. Example 6 • These are not mutually exclusive because an ace can be aheart. So we need to avoid double counting!

  14. Example 7 • A jar contains five red tokens and four black tokens. A token is drawn at random from the jar and then replaced; then another token is picked. What is the probability that both tokens are red?

  15. Example 7 • P(R,R)=

  16. Birthday Paradox • What is the probability that in a class of 35 students, at least two have the same birthday?

  17. Birthday Paradox Answer: • It’s reasonable to assume that the 35 birthdays are independent and that each day of the 365 days in a year is equally likely as a date of birth. (We ignore February 29.) Let E be the event that two of the students have the same birthday. It is tedious to list all the possible ways in which at least two of the students have matching birthdays. So, we consider the complementary event E’, that is, that no two students have the same birthday. • To find this probability, we consider the students one at a time. The probability that the first student has a birthday is 1, the probability that the second has a birthday different from the first is 364/365, the probability that the third has a birthday different from the first two is 363/365, and so on down to 331/365. Thus

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