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# Probability and simulating files for promotion

Individually remove all four aces from a deck of playing cards. There will now be 24 red cards in the deck, that will represent "male" files, and 24 black cards that will represent "female" files. Alternatively, you may use 48 index cards, marking half with "M" and half with "F". Shuffle the cards at least seven times and then cut them.

a. Count out the first 35 cards to represent the files recommended for promotion.

(i) What was the probability that a male will be promoted?
A female?
21 males and 14 females?
(a) in the first single simulation
(b) when considering the 100 repetitions as a whole.

(ii) Do you believe that your simulation provides evidence that the bank supervisors were biased against females?

(iii) How confident are you in your statement (iv)? Discuss how your expectation may have changed as you gained more information (in the form of empirical results).

#### Solution Preview

We took a sample of 35 cards from a deck. This represents a sample of files of people recommended for promotion. There is an equal number of black and red cards, meaning that there is a 50% chance that any individual file will be a male and a 50% chance that it will be a female.

Count out the first 35 cards to represent the files recommended for promotion.

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(i) What was the probability that a male will be promoted? A female?

I'm assuming that all 35 of the people who have their files drawn will be promoted. So, the probability that a male will be promoted is equal to the probability that at least one of the 35 files belongs to a man.

This is an example of a binomial experiment. Use the binomial formula to find the probability that at least one of the 35 people is a man (http://www.mathwords.com/b/binomial_probability_formula.htm). Unfortunately, the formula can only tell us the probability of choosing a certain number (not the probability of choosing at least a certain number). What we can do is determine the probability of not choosing any men, then subtracting that number from 1. This will give use the ...

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