attachment #2

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" () and "tails" () which we write , , etc. For each outcome, let be the random variable counting the number of tails in each outcome. For example, if the outcome is , then . Suppose that the random variable is defined in terms of as follows: . The values of are thus:

Outcome
Value of

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" () and "tails" () which we write , , etc. For each outcome, let be the random variable counting the number of tails in each outcome. For example, if the outcome is , then . Suppose that the random variable is defined in terms of as follows: . The values of are thus: Outcome Value of Calculate the probability distribution function of , i.e. the function . First, fill in the first row with the values of . Then fill in the appropriate probabilities in the second row.

Value of x of X	___?	____?	___?
Px(x)	___?	___?	___?

An employer interviews people for customer service positions in a company, and of the people are women. If all are qualified, in how many ways can the employer fill the customer service positions if exactly is a woman?

A fair die is rolled times. What is the probability of having no and no among the rolls? Round your answer to three decimal places.

Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of customers at Anita's, exactly order their food to go? Round your response to at least three decimal places.

An urn contains black and red balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all balls drawn from the urn are red? Round your answer to three decimal places.

At a certain fast-food restaurant, % of customers order a chicken sandwich, % of customers order french fries, and % of customers order a chicken sandwich or french fries (or both items). What is the probability that a randomly selected customer will order both a chicken sandwich and french fries?

Write your answer as a decimal (not as a percentage).