Probability of Compound Events

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Show your work for each problem.

1.
You flip a coin and roll a die. What is the probability of getting heads AND rolling a 4?
1. a)
2. b)
3. c)
4. d)
2.
Which formula is used for independent events?
1. a)
2. b)
3. c)
4. d)
3.
What is the probability of rolling a 2 OR a 5 on a single die? Give your answer as a simplified fraction (e.g., 1/3).
4.
Drawing a card from a deck, putting it back, then drawing another card. Are these events independent or dependent?
1. a)Mutually exclusive
2. b)Dependent
3. c)Independent
4. d)Neither
5.
You roll two dice. What is the probability of getting a sum of 7? Give your answer as a simplified fraction.
6.
A bag has 4 red balls and 6 blue balls. You draw two balls without replacement. Find the probability that both balls are blue.
7.
A spinner has 4 equal sections: red, blue, green, yellow. You spin twice. What is the probability of landing on red both times?
1. a)
2. b)
3. c)
4. d)
8.
A coin is flipped 3 times. What is the probability of getting heads all 3 times? Give your answer as a simplified fraction.
9.
A box contains 3 red pens and 5 blue pens. You randomly pick one pen, do not replace it, then pick another. What is the probability of picking a red pen first AND a blue pen second?
10.
What does P(B|A) represent?
1. a)The probability of B given that A has occurred
2. b)The probability of A and B
3. c)The probability of A given that B has occurred
4. d)The probability of A or B
11.
A jar has 7 green marbles and 3 yellow marbles. You draw 3 marbles without replacement. What is the probability that all 3 are green?
12.
A password consists of 2 digits (0-9). What is the probability of guessing the password correctly on the first try? Give your answer as a simplified fraction.
13.
In a class of 30 students, 12 play soccer and 8 play basketball. If the events are independent, what is the probability that a randomly selected student plays both sports?
14.
A test is 90% accurate. If you take the test twice (independently), what is the probability that both tests are correct?
1. a)95%
2. b)81%
3. c)180%
4. d)90%
15.
A bag contains 5 red, 4 green, and 3 blue marbles. You draw 2 marbles without replacement. What is the probability of drawing one red and one green marble (in any order)?