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Chapter 5: Q 4. (page 294)

Texas hold 鈥檈m In popular Texas hold 鈥檈m variety of poker, players make their best five-card poker hand by combining the two cards they are dealt with

three of five cards available to all players. You read in a book on poker that if you hold a pair (two cards of the same rank) in your hand, the probability of getting four of a kind is 88/1000

(a) Explain what this probability means.

(b) Why doesn鈥檛 this probability say that if you play

1000 such hands, exactly 88will be four of a kind?

Short Answer

Expert verified

Part (a) Out of 1000poker hands with a pair, around 88of them have a four of a kind.

Part (b) Out of 1000poker hands with a pair, we estimated that 88of them contained a four of a kind.

Step by step solution

01

Part (a) Step 1. Given Information

Getting four of a kind has a 0.25chance of happening.

02

Part (a) Step 2. Concept

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The probability of a chance outcome is its long-run relative frequency.

03

Part (a) Step 3. Explanation

The probability mentioned in the question is 88/1000, which suggests that out of every 100 poker hands with a pair, we should expect 88 of them to have a four-of-a-kind. This is the meaning of the probability given in the question for various Texas hold 'em poker games.

04

Part (b) Step 1. Explanation

This probability does not guarantee that out of 1000 such hands, exactly 88 will be four of a kind because it is also possible that 87 or 89 will be four of a kind. The number of fours of a kind is usually close to 88, but it isn't always exactly 88.

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Most popular questions from this chapter

Government data show that 8% of adults are full-time college students and that 30% of adults are age 55 or older. Since (0.08)(0.30)=0.024, can we conclude that about 2.4% of adults are college students55 or older? Why or why not?

Probability models? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give specific reasons for your answer.

(a) Roll a die and record the count of spots on the up-face: P(1) = 0, P(2) = 1/6, P(3) = 1/3, P(4) = 1/3,

P(5) = 1/6, P(6) = 0.

(b) Choose a college student at random and record gender and enrollment status: P(female full-time) = 0.56, P(male full-time) = 0.44, P(female part-time) = 0.24, P(male part-time) = 0.17.

(c) Deal a card from a shuffled deck: P(clubs) = 12/52, P(diamonds) = 12/52, P(hearts) = 12/52,

P(spades) = 16/52.

Roulette, An American roulette wheel has38slots with numbers 1through 36,0,and00,as shown in the figure. Of the numbered slots, 18are red, 18are black, and 2鈥攖丑别 0and 00鈥攁re green. When the wheel is spun, a metal ball is dropped onto the middle of the wheel. If the wheel is balanced, the ball

is equally likely to settle in any of the numbered slots. Imagine spinning a fair wheel once. Define events B: ball lands in a black slot, and E: ball lands in an even numbered slot. (Treat 0and 00as even numbers.)

(a) Make a two-way table that displays the sample space in terms of events B and E.

(b) Find P(B) and P(E).

(c) Describe the event 鈥淏 and E鈥� in words. Then find P(B and E). Show your work.

(d) Explain why P(B or E) 鈮� P(B) + P(E). Then use the general addition rule to compute P(B or E).

Due to a hit, A very good professional baseball player gets a hit about 35% of the time over an entire season. After the player failed to hit safely in six straight at-bats, a TV commentator said, 鈥淗e is due for a hit by the law of averages.鈥� Is that right? Why?

Find the probability that the computer is a laptop. Show your work.
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