Pre-Calculus
Probability Unit Review Sheet
Name: _____________________________________
For numbers 1 – 4, suppose a card is drawn from a well-shuffled standard deck of 52 cards. Find the probability of drawing each of
the following.
1. a spade.
2. a black face card.
3. not a black jack.
4. a black diamond.
5. One of the integers between 11 and 20, inclusive, is picked at random. What is the probability that the integer is:
a) even?
b) divisible by 3?
c) a prime?
d) odd?
Use the following information for numbers 6 – 8: you have an equally likely chance of spinning any value on the spinner. Find the
probability of spinning the given event.
6. a factor of 27.
7. a prime number.
9
4
5
2
8. a two digit number.
9. A pet store has 46 dogs. Twenty-two are brown and 36 are white. Seventeen are both brown and white. Find the probability that a
randomly chosen dog will be white or brown.
10. A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a three or a four?
11. A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a face card or red?
For numbers 12 – 14, find the indicated probability.
12. P(A) = 0.25, P(B) = 0.2, P(A and B) = 0.15, P(A or B) = ________
13. P(A) =
1
2
1
, P(B) = , P(A and B) = ________, P(A or B) =
2
5
10
14. P(A) = 99%, P(A') = _______
For numbers 15 – 17, find the probability of randomly drawing the given marbles from a bag of 4 red, 6 green, and 2 blue marbles
(a) with replacement and (b) without replacement.
15. a red, then a green
16. a blue, then a red
17. a red, then a red
Use the following information for numbers 18 – 25: You have an equally likely chance of rolling any value on each of two dice. Find
the probability of the given event.
18. Rolling a sum of either 4 or 10.
19. Rolling a sum less than 9.
20. Rolling a sum greater than or equal to 9.
21. Rolling a sum that is not 8 or 10.
22. Rolling a sum that is less than 6 or odd.
23. Rolling a sum that is a multiple of 3 and a multiple of 4.
24. Rolling a sum that is a multiple of 5.
25. Rolling a sum that is not 3.
Use the following information for numbers 26 – 29: A jar contains 30 green marbles, 20 black marbles, and 10 yellow marbles. Find
the probability of choosing the given marbles from the jar (a) with replacement and (b) without replacement.
26. Green, then black.
27. Yellow, then yellow.
28. Green, then black, then yellow.
29. Black, then black, then green.
Use the following information for numbers 30 – 33: Four marbles are chosen at random from a jar containing 15 red marbles and 10
blue marbles.
30. What is the probability that the selection will contain at least one red marble?
31. What is the probability that the selection will contain at least one blue marble?
32. What is the probability that the selection will contain exactly one red marble?
33. What is the probability that the selection will contain exactly two blue marbles?
Use the following information for numbers 34 – 37: Three cards are drawn from a standard 52 card deck. Find the probability of the
following.
34. There are 2 kings and 1 other card.
35. All the cards are black.
36. There is 1 ace and 2 other cards.
37. Two of the cards are even and one is odd.
38. You randomly select two cards from a standard deck of 52 cards. What is the probability that the first card is a seven or an ace and
the second card is a seven, ace, or queen if you replace the first card before selecting the second?
39. You randomly select two cards from a standard deck of 52 cards. What is the probability that the first card is a seven or an ace and
the second card is a seven, ace, or queen if you do not replace the first card before selecting the second?
40. The letters of the word ABRACADABRA are written on separate slips of paper and placed in a hat. Five slips of paper are then
randomly drawn, one after the other and without replacement. What is the probability of getting:
a) all A’s?
b) both R’s?
c) at least one B?
d) one of each letter?
41. a) The letters of the word TUESDAY are put into a bag. If three letters are taken out and not replaced, what is the probability the
three letters are S, D, and E, in that order?
b) The following letters STODUN are put into a bag. If all the letters are taken out and not replaced, what is the probability that the
order you take them out spells DONUTS?
For numbers 42 – 47, use the tree diagram to the right to find each probability.
42. P(S )
0.7
43. P(L | R)
R
0.3
44. P(J and R )
46. P(J and S)
0.5
0.2
45. P(R | J)
J
S
K
L
J
0.4
K
L
47. P(S | J)
For numbers 48 and 49, you toss a coin 3 times. Find the probability of the given event.
48. You toss exactly 1 tail.
49. You toss at least 1 tail.
For numbers 50 – 54, calculate the probability of tossing a coin 10 times and getting the given number of tails.
50. 3
51. 5
53. 6
54. 1
52. 9
55. Calculate the probability of randomly guessing at least 7 correct answers on a 10-question true-or-false quiz to get a passing grade.
56. Find the expected value:
x
P(x)
–4
0.2
–2
0.3
0
0.1
57. Find the expected value:
1
0.2
3
0.2
x
P(x)
–2
0.25
–1
0.35
0
0.05
1
0.15
3
0.2