different balls are randomly chosen from an urn containing 3 white, 3 red, and 5 black balls

different balls are randomly chosen from an urn containing 3 white, 3 red, and 5 black
balls

1. Three different balls are randomly chosen from an urn containing 3 white, 3 red, and 5 black
balls. Suppose that we win $1 for each white ball selected and lose $1 for each red selected.
Choosing a black ball yields $0. If we let X denote our total winnings from the experiment:
(a) Create a PMF for X.
(b) What is the probability we win money?
2. A school class of 120 students are driven in 3 buses to a symphonic performance. There are
36 students in one of the buses, 40 in another, and 44 on the third bus. When the buses
arrive, one of the 120 students is randomly chosen. Let X denote the number of students
on the bus of that randomly chosen student. What is E(X)?
3. The discrete random variable W has a PMF described by the table below.

(a) What is the probability that W is no more than 50?
(b) Given that W is at least 40, what is the probability that W is at least 60?
(c) Let Z = 0.05 *W. Find the PMF of Z.
4. Sarah is examining the concession stands before going to watch a movie. She is unusually
hungry today, but that doesn’t necessarily mean she will buy anything. The probability
that she buys candy is 0.70. If she buys candy, there is a 0.40 probability that she will also
buy popcorn and soda, and a 0.60 probability that she will buy neither. If she does not buy
candy, she will buy popcorn and soda with probability 0.80 and neither with probability
0.20. Let W represent the number of items (candy, popcorn, soda) that she purchases. Find
the PMF of W.
5. While visiting a foreign city, you are presented with the following game. The game has three
rounds of rolling a fair die. If you get a ‘1’ on the first roll, you win $12 and the game ends.
If you do not win on the first roll, then if you roll a ‘2’ on the second roll, you win you $9
and the game ends. If you still have not won, you get one last chance. If you get a ‘3’ on
the final roll, you win $6.
This game costs $4. Assume profitability is your only concern. Should you play?

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