### MAT 119 7.4 Using Counting Techniques in Probability

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TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. Four cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. (Round your answer to four decimal places.)

Four cards of the same suit are drawn.

1. Five balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability of the given event. (Round your answer to three decimal places.)

Two or three of the balls are white.

1. Assume the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with three children will have the given composition.

The two oldest children are girls.

1. Jacobs & Johnson, an accounting firm, employs 17 accountants, of whom 9 are CPAs. If a delegation of 3 accountants is randomly selected from the firm to attend a conference, what is the probability that 3 CPAs will be selected?

1. A customer from Cavallaro's Fruit Stand picks a sample of 5 oranges at random from a crate containing 80 oranges, of which 6 are rotten. What is the probability that the sample contains 1 or more rotten oranges? (Round your answer to three decimal places.)

2. Electronic baseball games manufactured by Tempco Electronics are shipped in lots of 20. Before shipping, a quality-control inspector randomly selects a sample of 6 from each lot for testing. If the sample contains any defective games, the entire lot is rejected. What is the probability that a lot containing exactly 3 defective games will still be shipped? (Round your answer to three decimal places.)

3. A student studying for a vocabulary test knows the meanings of 10 words from a list of 22 words. If the test contains 10 words from the study list, what is the probability that at least 8 of the words on the test are words that the student knows? (Round your answer to three decimal places.)

4. In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (Round your answers to four decimal places.)

(a) If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?

(b) If a player is dealt 2 cards from 2 well shuffled standard decks, what is the probability that the player will receive a blackjack?

1. A world record was set in a given year for the longest run on an ungaffed (fair) roulette wheel. The number 28 appeared 5 times in a row. What is the probability of the occurrence of this event? (Assume that there are 38 equally likely outcomes consisting of the number 1-36, 0, and 00. If you enter your answer in scientific notation, round the decimal value to two decimal places. Use equivalent rounding if you do not enter your answer in scientific notation.)

2. A list of poker hands, ranked in order from the highest to the lowest, is shown in the accompanying table along with a description and example of each hand. Use the table to help you answer the question.

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand? (Round your answer to five decimal places.)

A straight (but not a straight flush)

1. A list of poker hands, ranked in order from the highest to the lowest, is shown in the accompanying table along with a description and example of each hand. Use the table to help you answer the question.

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand? (Round your answer to five decimal places.)

Two pairs

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