6. You are the sales manager for a large high-end clothing store. You have a tot
ID: 3064370 • Letter: 6
Question
6. You are the sales manager for a large high-end clothing store. You have a total 100 salespeople at the store, and 30 of them sold $1000 or less yesterday while the rest sold over $1000. Among the salespeople who sold $1000 or less, there is a probability of 0.30 that the salesperson is new (less than one year on the job), while among the salespeople who sold over $1000 there is a probability of 0.10 that the salesperson is new. Given that a salesperson is new, what is the probability that the salesperson sold over $1000? 7. The standard version of the game of poker is played with a deck of 52 different playing cards and a poker player is given five cards at random without replacement as a poker hand. The order in which the cards are chosen does not matter. How many different standard poker hands are possible? Fortune magazine publishes an annual list of the 500 largest companies in the United States. In 2016, twenty-three of these companies had revenues of over $100 billion. If a company on the 2016 Fortune 500 list is chosen at what is the probability that it had revenues of over $100 billion? 8. random,Explanation / Answer
6)
A - sold less than 1000
B - sold over 1000
X - salesperson is new
P(A) = 0.3
P(B) = 0.7
P(X|A) = 0.30
P(X|B) = 0.10
P(B|X) = P(B and X) /P(X)
= P(B) P(X|B) / (P(B) P(X|B)+P(A) P(X|A))
= 0.70 * 0.10 / (0.7*0.1 + 0.3* 0.3)
= 0.4375
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