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Chapter 5: Q 9. (page 294)
Due to a hit, A very good professional baseball player gets a hit about 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?
It was not right.
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Recycling Do most teens recycle? To find out, an AP Statistics class asked an SRS of 100 students at their school whether they regularly recycle. How many students in the sample would need to say 鈥淵es鈥� to provide convincing evidence that more than half of the students at the school recycle? The Fathom dot plot below shows the results of taking 200 SRSs of 100 students from a population in which the true proportion who recycle is 0.50.
(a) Suppose 55 students in the class鈥檚 sample say 鈥淵es.鈥� Explain why this result does not give convincing evidence that more than half of the school鈥檚 students recycle.
(b) Suppose 63 students in the class鈥檚 sample say 鈥淵es.鈥� Explain why this result gives strong evidence that a majority of the school鈥檚 students recycle.
Monty Hall problem In Parade magazine, a reader posed the following question to Marilyn vos Savant and the 鈥淎sk Marilyn鈥� column: Suppose you鈥檙e on a game show, and you鈥檙e given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what鈥檚 behind the doors, opens another door, say #3, which has a
goat. He says to you, 鈥淒o you want to pick door #2?鈥� Is it to your advantage to switch your choice of doors? The game show in question was Let鈥檚 Make a Deal and the host was Monty Hall. Here鈥檚 the first part of Marilyn鈥檚 response: 鈥淵es; you should switch. The first door has a chance of winning, but
the second door has a chance.鈥� Thousands of readers wrote to Marilyn to disagree with her answer. But she held her ground.
(a) Use an online Let鈥檚 Make a Deal applet to perform at least repetitions of the simulation. Record whether you stay or switch (try to do each about half
the time) and the outcome of each repetition.
(b) Do you agree with Marilyn or her readers? Explain.
Tossing coins Refer to Exercise 40. Define event : get more heads than tails. Find .
Shuffle a standard deck of cards, and turn over the top card. Put it back in the deck, shuffle again, and turn over the top card. Define events : first card is a heart, and : second card is a heart.
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
(a) Explain what this probability means.
(b) Why doesn鈥檛 this probability say that if you play
1000 such hands, exactly will be four of a kind?
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