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1. Consider a regular six-sided die, but with non-standard numbering: the number 1 is on two of
its sides, the number 2 on another two sides, the number 3 on one side and the number 4 on
the remaining side.
a. If this die is rolled once, what is the probability of getting a 4? [2 points]
b. If this die is rolled once, what is the probability of getting a 1? [2 points]
c. If this die is rolled three times, what is the probability of getting a number less than 3
at least once? [6 points]
d. If the die is rolled three times, what is the probability of rolling a 1 followed by a 3
followed by a 2? [3 points]
2. Consider an urn containing 40 balls. Each ball is either blue or red. Each ball is stamped with
a number: either 1 or 2 or 3. There are exactly 24 blue balls in the urn. There are exactly 10
balls stamped with the number 1 in the urn. A ball has been selected “at random” from the
urn (i.e., each of the 40 balls has an equal chance of being selected). Let 𝐴 be the outcome
that this ball is stamped with the number 1. Let 𝐵 be the outcome that this ball is blue.
a. Calculate Pr(𝐴) and Pr(𝐵). Be sure to explain how you arrived at your answer.
[3 points]
b. Suppose that outcomes 𝐴 and 𝐵 are independent.
i. How many of the 24 blue balls are stamped with the number 1? Be sure to
explain your reasoning. [6 points]
ii. Let 𝐶 be the outcome that the selected ball is stamped with the number 2.
Suppose that exactly 8 of the 16 red balls are stamped with the number 2. If
outcomes 𝐵 and 𝐶 are independent, how many blue balls are stamped with
the number 2? Be sure to explain your reasoning. [Hint: You may find it
useful to review Slide 5 of Video A for Week 6.] [8 points]
3. For each of the following scenarios say whether or not it exhibits faulty reasoning about
probability. If you think it does, indicate whether it commits the Conjunction Fallacy or the
Gambler’s Fallacy. Be sure to explain your answer.
a. A large survey of NZ taxpayers classifies respondents as “poor” or “non-poor”, and as
“educated” or “non-educated”. The survey collects data on the prevalence of
workplace injury. Amongst respondents who are “poor and non-educated”, 30% had
suffered a workplace injury. Amongst “non-educated” respondents, only 10% had
suffered a workplace injury. If a randomly selected respondent is known to have
suffered a workplace injury, it is more likely that s/he is poor and non-educated than
that s/he is non-educated. [10 points]
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b. If a coin is tossed 4 times, the probability of getting an equal number of Heads and
Tails (i.e., 2 each) is higher than the probability of getting an unequal number of Heads
and Tails. [10 points]
4. The Black Ferns are scheduled to play the Wallaroos on Saturday. Suppose that the
probability of the Black Ferns winning the game is 0.6 if it rains and 0.8 if it does not rain.
The game is played under the ‘golden point’ rule so a draw is not possible (either the Black
Ferns will win or the Wallaroos will win). A meteorologist estimates that the probability of
rain on Saturday is 0.3. In answering the questions below, it may be helpful to let W denote
a win by the Black Ferns and R denote that it rained.
a. What is the probability that it will not rain on Saturday? [1 point]
b. What is the total probability that the Black Ferns will beat the Wallaroos?
[4 points]
c. What is the probability that the Wallaroos will beat the Black Ferns if (i) it rains, (ii) it
does not rain? [2 points]
d. Suppose you didn’t watch the game but you discover that the Black Ferns won.
What is the probability that it rained? [5 points]
e. Instead, suppose you discover that the Wallaroos won. What is the probability that
it rained? [5 points]
5. Suppose that one out of every 15,000 people is a genius and that an intelligence test can
identify a genius with 95% accuracy (i.e., 95% of people who pass the test are geniuses and
95% of people who fail the test are not geniuses). Emma passes the intelligence test and
claims, I am a genius!
a. What is the probability that Emma is a genius? [8 points]
b. Suppose that Emma does not understand equations. In simple terms, explain why it
is unlikely that Emma is a genius. [5 points]
6. Based on your experiences, explain how any of the two concepts below have influenced
your judgements. If your judgements have not been influenced by the concepts below,
explain how you avoid biases in your decision making. Word limit (for all parts): 400 words.
[20 points]
a. Confirmation bias
b. Availability bias
c. Overconfidence
d. Hindsight bias
e. Affect heuristic

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1. Consider a regular six-sided die, but with non-standard numbering: the number 1 is on two of its sides, the number 2 on another two sides, the number 3 on one side and the number 4 on the remaining side. a. If this die is rolled once, what is the probability of getting a 4? [2 points] b. If this die is rolled once, what is the probability of getting a 1? [2 points] c. If this die is rolled three times, what is the probability of getting a number less than 3 at least once? [6 points] d. If the die is rolled three times, what is the probability of rolling a 1 followed by a 3 followed by a 2? [3 points] 2. Consider an urn containing 40 balls. Each ball is either blue or red. Each ball is stamped with a number: either 1 or 2 or 3. There are exactly 24 blue balls in the urn. There are exactly 10 balls stamped with the number 1 in the urn. A ball has been selected “at random” from the urn (i.e., each of the 40 balls has an equal chance of being selected). Let 𝐴 be the outcome that this ball is stamped with the number 1. Let 𝐵 be the outcome that this ball is blue. a. Calculate Pr(𝐴) and Pr(𝐵). Be sure to explain how you arrived at your answer. [3 points] b. Suppose that outcomes 𝐴 and 𝐵 are independent. i. How many of the 24 blue balls are stamped with the number 1? Be sure to explain your reasoning. [6 points] ii. Let 𝐶 be the outcome that the selected ball is stamped with the number 2. Suppose that exactly 8 of the 16 red balls are stamped with the number 2. If outcomes 𝐵 and 𝐶 are independent, how many blue balls are stamped with the number 2? Be sure to explain your reasoning. [Hint: You may find it useful to review Slide 5 of Video A for Week 6.] [8 points] 3. For each of the following scenarios say whether or not it exhibits faulty reasoning about probability. If you think it does, indicate whether it commits the Conjunction Fallacy or the Gambler’s Fallacy. Be sure to explain your answer. a. A large survey of NZ taxpayers classifies respondents as “poor” or “non-poor”, and as “educated” or “non-educated”. The survey collects data on the prevalence of workplace injury. Amongst respondents who are “poor and non-educated”, 30% had suffered a workplace injury. Amongst “non-educated” respondents, only 10% had suffered a workplace injury. If a randomly selected respondent is known to have suffered a workplace injury, it is more likely that s/he is “poor and non-educated” than that s/he is “non-educated”. [10 points] b. If a coin is tossed 4 times, the probability of getting an equal number of Heads and Tails (i.e., 2 each) is higher than the probability of getting an unequal number of Heads and Tails. [10 points] 4. The Black Ferns are scheduled to play the Wallaroos on Saturday. Suppose that the probability of the Black Ferns winning the game is 0.6 if it rains and 0.8 if it does not rain. The game is played under the ‘golden point’ rule so a draw is not possible (either the Black Ferns will win or the Wallaroos will win). A meteorologist estimates that the probability of rain on Saturday is 0.3. In answering the questions below, it may be helpful to let W denote a win by the Black Ferns and R denote that it rained. a. What is the probability that it will not rain on Saturday? [1 point] b. What is the total probability that the Black Ferns will beat the Wallaroos? [4 points] c. What is the probability that the Wallaroos will beat the Black Ferns if (i) it rains, (ii) it does not rain? [2 points] d. Suppose you didn’t watch the game but you discover that the Black Ferns won. What is the probability that it rained? [5 points] e. Instead, suppose you discover that the Wallaroos won. What is the probability that it rained? [5 points] 5. Suppose that one out of every 15,000 people is a genius and that an intelligence test can identify a genius with 95% accuracy (i.e., 95% of people who pass the test are geniuses and 95% of people who fail the test are not geniuses). Emma passes the intelligence test and claims, I am a genius! a. What is the probability that Emma is a genius? [8 points] b. Suppose that Emma does not understand equations. In simple terms, explain why it is unlikely that Emma is a genius. [5 points] 6. Based on your experiences, explain how any of the two concepts below have influenced your judgements. If your judgements have not been influenced by the concepts below, explain how you avoid biases in your decision making. Word limit (for all parts): 400 words. [20 points] a. Confirmation bias b. Availability bias c. Overconfidence d. Hindsight bias e. Affect heuristic Name: Description: ...
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