Question 1

Suppose you plan to roll a six-sided die.
-Which of the following sequences of die rolls is the least likely to occur?
A) 1 - 1 - 1 - 1 - 1
B) 2 - 3 - 4 - 5 - 6
C) 1 - 5 - 2 - 1 - 3
D) All of the above sequences have the same probability.

Accepted Answer

Each sequence of die rolls is equally likely because each roll is independent and has a 1/6 probability for any specific outcome.

Question 2

Suppose you plan to roll a six-sided die.
-You plan to roll the die n times. With each roll, you record whether the die landed on an odd number or an even number. For which of the following values of n would you have the lowest probability of observing all even number rolls?
A) n = 2
B) n = 5
C) n = 20
D) n = 100

Accepted Answer

The probability of rolling an even number on a six-sided die is 1/2. The probability of rolling all even numbers decreases as n increases, so n = 100 has the lowest probability.

Question 3

The lottery game Powerball advertises that the probability of winning a prize is 0.04. This means that if 100 people play Powerball, then 4 of them will win a prize.

Accepted Answer

The probability of 0.04 means that, on average, 4 out of 100 people might win, but it does not guarantee that exactly 4 will win in every group of 100 players due to the randomness of each draw.

Question 4

The lottery game Powerball advertises that the probability of winning a prize is 0.04. This means that, in the long run, if thousands of people play Powerball, then about 4% of them will win a prize.

Accepted Answer

The probability of winning a prize in Powerball is 0.04, which means that statistically, 4% of players are expected to win a prize over a large number of trials.

Question 5

A classmate claims that he can smell the difference between a Starbucks cup of coffee and a Dunkin' Donuts cup of coffee. You decide to test this claim by blindfolding him and presenting him with two cups of coffee - one from Starbucks and one from Dunkin' Donuts.
-Your classmate guesses the correct brand of coffee both times in two trials. Does this convince you that your classmate's claim is true?
A) Yes, since the classmate was correct in 100% of the trials.
B) Yes, since if the classmate was just guessing, it is very unlikely to guess correctly twice in a row.
C) No, since if the classmate was just guessing, there is a 50% chance of guessing correctly twice in a row.
D) No, since if the classmate was just guessing, there is a 25% chance of guessing correctly twice in a row.

Accepted Answer

The answer of A classmate claims that he can smell...

Question 6

A classmate claims that he can smell the difference between a Starbucks cup of coffee and a Dunkin' Donuts cup of coffee. You decide to test this claim by blindfolding him and presenting him with two cups of coffee - one from Starbucks and one from Dunkin' Donuts.
-Your classmate guesses the correct brand of coffee in 65 out of 100 trials. Does this convince you that your classmate's claim is true?
A) No, since 65 out of 100 is close to 50%.
B) No, since the classmate did not guess correctly in all 100 trials.
C) Yes, since there is less than a 1% chance of guessing correctly in 65 or more of 100 trials if the classmate was just guessing.
D) Yes, since 65% is greater than 50%.

Accepted Answer

The probability of guessing correctly in 65 or more of 100 trials if the classmate was just guessing is less than 1%. This means that it is very unlikely that the classmate was just guessing, and that he is likely able to smell the difference between a Starbucks cup of coffee and a Dunkin' Donuts cup of coffee.

Quiz 1: Preliminaries: Introduction to Statistical Investigations

Suppose you plan to roll a six-sided die. -Which of the following sequences of die rolls is the least likely to occur?

Suppose you plan to roll a six-sided die. -You plan to roll the die n times. With each roll, you record whether the die landed on an odd number or an even number. For which of the following values of n would you have the lowest probability of observing all even number rolls?

The lottery game Powerball advertises that the probability of winning a prize is 0.04. This means that if 100 people play Powerball, then 4 of them will win a prize.

The lottery game Powerball advertises that the probability of winning a prize is 0.04. This means that, in the long run, if thousands of people play Powerball, then about 4% of them will win a prize.