Week 5 Quiz

You roll a fair six-sided die five times and never see a six. What is the probability that the sixth roll is a six?

Select one.

• More than 1 ⁄ 6, because a six is now due
• Exactly 1 ⁄ 6, because the die has no memory
• Less than 1 ⁄ 6, because this die seems to avoid sixes
• 5 ⁄ 6, because five of the six rolls missed

Two fair dice are rolled, giving 36 equally likely ordered outcomes, such as (4, 6) for a 4 on the first die and a 6 on the second. How many of the 36 outcomes give a sum of 10 or more? Enter a whole number only.

Type a short answer.

For a roll of two fair dice, let A be the event "the sum is 10 or more". Which event is the complement of A?

Select one.

• The sum is 9 or less
• The sum is 10 or less
• The sum is exactly 9
• The sum is 12

Two fair dice are rolled. The event "the first die shows 6" has 6 of the 36 outcomes, the event "the sum is 10 or more" has 6 of the 36 outcomes, and the outcomes (6, 4), (6, 5), and (6, 6) belong to both. What is P(first die 6 or sum ≥ 10)?

Select one.

• 12 ⁄ 36
• 3 ⁄ 36
• 9 ⁄ 36
• 6 ⁄ 36

A student guesses at random on two four-option multiple-choice questions, and each guess picks the keyed option with probability 1 ⁄ 4 = 0.25. The two guesses do not affect each other. What is the probability that both guesses pick the keyed option?

Select one.

• 1 ⁄ 2
• 1 ⁄ 4
• 1 ⁄ 8
• 1 ⁄ 16

The table below counts the 344 penguins in the Palmer field log by species and island. A penguin is chosen at random from the log. What is P(the penguin is Gentoo | the penguin is on Biscoe)?

Select one.

• 124 ⁄ 168 ≈ 0.7381
• 124 ⁄ 344 ≈ 0.3605
• 168 ⁄ 344
• 124 ⁄ 124 = 1

In the Palmer penguins field log, every one of the 124 Gentoo penguins was logged on Biscoe, which holds 168 penguins in all. True or false: P(Biscoe | Gentoo) is equal to P(Gentoo | Biscoe).

True or false.

• True
• False

Select every pair of events below that are independent.

Select every option that applies.

• Two dice: "the first die shows 6" and "the second die shows 6"
• Two dice: "the first die shows 6" and "the sum is 7"
• Two dice: "the first die shows 6" and "the sum is 10 or more"
• One penguin from the field log: "it is Adelie" and "it is Gentoo"

In the Palmer field log, P(Gentoo | Biscoe) ≈ 0.7381 while P(Gentoo) ≈ 0.3605, so species and island are not independent. The log comes from an observational study. Which conclusion do these numbers support?

Select one.

• Living on Biscoe causes a penguin to become Gentoo
• Species and island have no relationship in this log
• Species and island are associated, and the data alone do not show cause
• Gentoo penguins would become Adelie if moved to Torgersen

In the Palmer field log, Biscoe holds 44 Adelie and 124 Gentoo penguins and no Chinstrap penguins. Which statement describes the conditional distribution of species among the Biscoe penguins?

Select one.

• Of 344 penguins, 152 are Adelie, 68 Chinstrap, and 124 Gentoo
• Of 168 Biscoe penguins, 44 are Adelie and 124 are Gentoo
• Of 124 Gentoo penguins, all 124 are on Biscoe
• Of 168 Biscoe penguins, about one third are Gentoo