Introduction to Probability Distributions

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Show your work for each problem.

1.
For a valid probability distribution, all probabilities must sum to:
1. a)100
2. b)1
3. c)0
4. d)It depends on the number of outcomes
2.
What is the probability of rolling any number on a fair 6-sided die?
1. a)
2. b)
3. c)
4. d)
3.
If the probabilities in a distribution are , , and , what probability is missing?
4.
Which type of distribution has all outcomes with equal probability?
1. a)Poisson distribution
2. b)Uniform distribution
3. c)Normal distribution
4. d)Binomial distribution
5.
How many total outcomes are possible when rolling two dice?
6.
What is the probability of rolling a sum of 7 with two dice? Write as a simplified fraction (e.g., 1/6).
7.
When rolling two dice, which sum is MOST likely?
1. a)12
2. b)7
3. c)2
4. d)6
8.
A bag contains 3 red, 2 blue, and 5 green marbles. Create a probability distribution for drawing one marble.
9.
Calculate the expected value when rolling a fair die.
10.
A game costs 5 euros to play. You win 20 euros if you roll a 6, otherwise you win nothing. What is the expected profit per game?
1. a) euros
2. b) euros (about euros)
3. c) euros
4. d) euros (about euros)
11.
A factory produces items with a 4% defect rate. In a batch of 250 items, what is the expected number of defective items?
12.
A coin is biased so that P(heads) = 0.6 and P(tails) = 0.4. If heads wins 3 euros and tails loses 2 euros, what is the expected value per flip?
13.
A lottery ticket costs 2 euros. You have a 1% chance to win 100 euros, 5% chance to win 10 euros, and otherwise win nothing. Is this a fair game?
14.
Which statement about expected value is FALSE?
1. a)Expected value can be negative
2. b)Expected value is always one of the possible outcomes
3. c)Expected value represents the long-run average
4. d)Expected value is a weighted average of outcomes
15.
An insurance company knows that 2% of customers file claims averaging 8000 euros. They charge each customer a 200 euro annual premium. With 5000 customers, what is their expected annual profit?