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1) Fourteen red marbles and sixteen green marbles are in a bag. Two marbles are picked out one at a time and replaced after they are picked. Build a tree diagram and probability model to show the different combinations of marbles that could be pulled out of the bag.
2) A bag contains a standard set of pool balls. Two balls are pulled out, one after another, and not replaced. What is the probability that the two balls are a solid and a striped ball in either order? (Recall that there are 8 solid pool balls and 7 striped pool balls.)
3) A bag contains a $100 bill and two $20 bills. A second bag contains 1 gold marble and 2 silver marbles. You get to pick one bill out of the first bag. After this, you pick a marble out of the second bag. If you get the gold marble, you get to triple the amount of money you pulled from the first bag. If you get a silver marble, you get to double the amount of money you picked from the first bag. Build a probability model for all the different amounts of money that you might win.
4) A basketball player is practicing shooting free throws. Suppose she makes 75% of her free throw attempts. Make a tree diagram and probability model for what might happen if she decides to shoot three free throws. In other words, what is the probability that she makes zero shots, one shot, two shots, or all three shots.
5) A coin is flipped and then two dice are rolled. Build a probability model that shows how likely it is to get heads followed by doubles, heads and a non-doubles, tails and doubles, and tails and non-doubles.
6) A spinner with four evenly-spaced wedges of red, blue, green, and orange on it is spun and a coin is flipped.
a) How many different outcomes are possible?
b) Build a probability model that shows the probabilities for each outcome.
7) A baseball player is a .400 hitter. This means that he gets a hit (single, double, triple, or home run) 40% of the time he has an at-bat. Use a tree diagram to build a probability model that shows the probability of the player having 0, 1, 2, or 3 hits if he has 3 at-bats in one game.
8) In some sports, the home team wins a higher percentage of games played. Suppose the Dunkers and the Hoopsters are playing a best-of-three game series against each other. When the Dunkers are home, they have a 60% chance of winning a game against the Hoopsters. When the Hoopsters are home, they have a 55% chance of winning a game against the Dunkers. The Dunkers will be the home team in games 1 and 3 while the Hoopsters will be the home team in game 2. Use a tree diagram to build a probability model for this situation. The model should show the chances that the Dunkers win in 2 games or in 3 games and the chances that the Hoopsters win in 2 games or in 3 games.
9) A patient is scheduled to have two surgeries. The results of each surgery are independent of each other. Suppose the first surgery has a 90% success rate and the second surgery has an 85% success rate. Build a probability model by using a tree diagram that shows all the different results that might occur.
10) A bag contains ten red cubes numbered 1 through 10 and five blue cubes numbered 1 through 5. You pull two cubes out of the bag without replacement. What is the probability that the two cubes will be an odd cube and a red cube (in either order)?
Review Exercises
11) Suppose events 'A' and 'B' are mutually exclusive and that P(A)=0.35 and P(B)=0.14. What is P(A or B)?
12) How many unique three-letter 'words' can be formed by selecting three letters from the alphabet if no letter may be repeated?
13) How many unique three-letter 'words' can be formed by selecting three letters from the alphabet if letters may be repeated?
14) 20% of all households in the Twin Cities get the Star Tribune newspaper delivered to their home while only 15% get the Pioneer Press delivered to their home. If 70% of homes do not get either newspaper delivered, what percent of homes get both newspapers delivered?
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