Department

EconomicsCourse Code

ECON 15AProfessor

Paul ShireyStudy Guide

MidtermThis

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TEST THREE

PROBABILITY AND STATISTICS, ECON 15A

NOVEMBER 9, 2018

If the answer is most easily expressed with fractions, please use them, and keep the answer in unsolved, un-simplified form,

e.g. 4/52 x 3/51 x 2/50. If the answer is decimal to begin with, solve it, and give a decimal answer. Show work, even if it is obvious.

1. In a certain business there are bosses and workers, women and men. If a person is picked at random, the probability of being a boss

is .20. If a person is picked at random, the probability of being a woman is .40. Fill in the below table’s joint probabilities, assuming

work status and gender are independent.

Bosses Workers

Women

Men

2. If the probability of picking someone who is a woman and a boss is .10, what is the probability of picking someone who is either a

woman or a boss?

3. What is the probability of picking a male worker?

4. What is the probability of picking a boss given that the person is a woman?

5. What is the probability of picking a boss given that the person is a man?

6. Your friend claims to be a magician. He hands you two cards – the first, a king of hearts; the second a queen of hearts. Your friend

tells you not to show him the cards, and puts them back in the pile of cards. He shuffles the cards and discards two. He claims these are

the ‘sacrifices’ to the gods, so that he can ‘find’ your cards – the king of hearts at the top of the deck, and the queen of hearts on the

bottom of the deck. Assuming your friend has no magical ability (real or illusionary), what is the probability he pulls the correct cards.

[A note to the student who wrote this question: your answer was incorrect.]

7. You are spinning a wheel of fortune that is split into four equal parts. Their colors are green, blue, red, and purple. If you spin the

wheel twice, what is the probability of it landing on blue on the first spin and purple on the second spin?

8. Mark, Carmen, Holly, and Jacob all go to a magic show. The magician has them each pick and keep one card. He states that after

saying the magic word, they will flip over their card and every card will be a “10.” What is the probability this is true?

9. Five cards are dealt. The first three are not the queen of hearts. What is the probability that the queen of hearts is one of the cards

dealt.

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