AP Stats Lesson 5.1 Homework

1. In a New York Times article, an analyst stated that the probability of a legal dispute ending in a settlement, rather than going to trial, is around 0.90. What does this probability indicate?

• There is a 90% chance that a legal dispute will end in a settlement.

• There is a 10% chance that a legal dispute will end in a settlement.

• There is a 90% chance that a legal dispute will go to trial.

• There is a 10% chance that a legal dispute will go to trial.

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CCSS.7.SP.C.5

2a. Paul flipped a fair coin 10 times. How many of the coin flips would you expect to land on 'Tails'? Is this result guaranteed?

• 5, Yes

• 5, No

• 10, Yes

• 10, No

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CCSS.7.SP.C.6

What proportion of Paul's flips resulted in a Tail? Is this result surprising? Explain.

• 0.5, Yes, because the probability of getting tails is usually 0.5.

• 0.6, No, because the probability of getting tails is usually 0.5.

• 0.7, Yes, because the probability of getting tails is usually 0.5.

• 0.8, No, because the probability of getting tails is usually 0.5.

2c. How do you think the proportion of tails would change if Paul flipped the coin 200 times?

• The proportion of tails would increase.

• The proportion of tails would decrease.

• The proportion of tails would remain approximately the same.

• The proportion of tails would become unpredictable.

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CCSS.7.SP.C.6

3a. Which of the following events has a probability of 0.25?

• Rolling a 3 on a standard six-sided die

• Drawing a heart from a standard deck of cards

• Flipping a coin and getting heads

• Choosing a red marble from a bag with 3 red and 9 blue marbles

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CCSS.7.SP.C.7A

3b. Give an example of an event that has a probability of 0.

• Rolling a 7 on a standard 6-sided die

• Drawing a red card from a standard deck of cards

• Flipping a coin and getting heads

• Rolling an even number on a standard 6-sided die

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CCSS.7.SP.C.5

3c. Which of the following events has a probability of 1/3?

• Rolling a 2 on a standard six-sided die

• Drawing a red card from a standard deck of cards

• Choosing a blue marble from a bag with 2 red, 1 blue, and 3 green marbles

• Flipping a coin and getting heads

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CCSS.7.SP.C.7A

3d. Which of the following is an example of an event that has a probability of 1?

• Rolling a 7 on a standard six-sided die

• The sun rising in the east

• Flipping a coin and getting heads

• Drawing a red card from a standard deck of cards

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CCSS.7.SP.C.5

Carly's teacher gives each student a playing card at the beginning of class to determine what table they will sit at for the day (all students with a '3' sit at one table, all students with a 'queen' sit at one table, etc.). Carly ended up at a table with her best friend on Monday and Tuesday. On Wednesday, Carly thinks there is no way she will be at the same table as her friend AGAIN. Why is Carly's thinking flawed?

• Because the cards are shuffled randomly each day, so past outcomes do not affect future ones.

• Because there are only a few tables, so it's likely to happen again.

• Because her teacher might intentionally place them together.

• Because Carly and her friend always pick the same card.

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CCSS.RI.8.1

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Francine's favorite Spotify playlist has 35 songs on it, which are sorted by date added. She listens to the playlist on shuffle mode. At one point Francine noticed that songs 7, 8, and 9 on the playlist played back-to-back. She is convinced that the shuffle mode isn't actually random. Do you agree? Explain.

• Yes, because the probability of consecutive songs playing is very low.

• No, because random sequences can still have patterns.

• Yes, because shuffle mode should never play consecutive songs.

• No, because the playlist is too small for true randomness.

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CCSS.7.SP.B.3