Probability Learning Self-Quiz
Green: A card is drawn from a single deck of 52 cards.
1.
2.
3.
4.
Find the probability of drawing a club.
Find the probability of drawing a card that is black or a number 10 (or both).
Find the probability of drawing a picture card (includes jack or queen or king).
Find the probability of drawing a red ace.
Green: Combo sample space
A die is thrown and a coin is flipped.
What is the probability of landing a heads and rolling an even number?
Blue: A box contains 1 red marble, 2 white marbles, 3 green marbles. Two marbles are drawn at
random without replacement. Find the probability of:
1.
2.
3.
4.
5.
Selecting a green marble in a second draw if the first marble is red.
Selecting a white marble in the first draw and red marble in a second draw.
Selecting red marbles in both draws.
Selecting red or white in a first draw and green or white in a second draw.
Selecting white marble in a first draw and white or green in a second draw.
17. A drawer contains eight red, eight yellow, eight green and eight black socks. What
is the probability of getting at least one pair of matching socks when five socks are
randomly pulled from the drawer?
18. A drawer contains 2 brown and 3 gray socks. The socks are taken out of the drawer
one at a time. What is the probability that the fourth sock removed is gray?
Express your answer as a common fraction.
Black:
Odds (not hard – just to make sure you understand “odds”)
Mark Louis high school plans for a field trip and a month is selected at random. School is closed on June
and July for summer holidays. Exams will be conducted in May every year.
1. Find the odds in favor of selecting a month ends with Y.
2. Find the odds against a month start with J.
Some difficult challenges like normal black problems
38. A bag contains six white marbles, five red marbles and four blue marbles. Norka will
reach into the bag and pull out three marbles at the same time. What is the
probability that all three marbles will be the same color? Express your answer as a
common fraction.
45. Five girls are each given two standard dice. Each of the girls rolls her pair of dice
and writes down the product of the two numbers that she rolled. What is the
probability that all of the girls have written down a product greater than 10?
Express your answer as a decimal to the nearest ten thousandth.
52. Five of the 50 computers in a lab have a virus. Ten of the computers are selected at
random. What is the probability that none of the selected computers are infected?
Express your answer as a decimal to the nearest hundredth.
SOME SOLUTIONS
BLACK
38. There are 6 + 5 + 4 = 15 marbles in the bag. Norka will be happy is she gets three white, three red or three blue.
The probability of getting three white is 6/15 x 5/14 x 4/13 = 120/2730. The probability of getting red is 5/15 x
4/14 x 3/13 – 60/2730. The probability of getting three blue is 4/15 x 3/14 x 2/13 = 24/2730. Adding these three
different ways to get three marbles of the same color, we get a total probability of (120 + 60 + 24)/2730 =
204/2730 = 34/455.
45. There are three 36 ways that two standard dice and land. The possible products of the two dice range from 1 x 1 =
1 to 6 x 6 = 36. Seventeen of these 36 products are greater than 10; thus, each of the five girls has a 17/36
probability of getting a product greater than 10. To calculate the probability that all five of the girls roll their dice
and each of them gets a product greater than 10, we multiply their individual probabilities. We get (17/36) x
(17/36) x (17/36) x (17/36) x (17/36) or (17/36)5 ≈ 0.0235 to the nearest ten thousandth.
52. If the virus is not detected by the test, then none of five infected computers were among the ten tested. That
means that the ten tested computer were among the 45 uninfected ones. The chance that the first computer
tested is uninfected is
45
44
45 44
, that the second is also uninfected
and that both are uninfected is
.
x
50
49
50 49
Continuing in the same way, the probability that none were infected is
45 44 43 42 41 40 39 38 37 36
x
x
x
x
x
x
x
x
x
 0.31
50 49 48 47 46 45 44 43 42 41
BLUE
17. The probability of getting at least one pair of matching socks is 1. Even if the first four socks chosen
are all different colors, the fifth sock will match one of them because there are only four colors.
18. There are 5C2 = 10 possible outcomes, and they can be listed easily, GGGBB, BGGGB, GGBGB, GBGGB,
BBGGG, BGGBG, BGBGG, GBGBG, GBBGG, GGBBG. Out of the ten outcomes, the fourth sock removed is
6 3
grey in six of them. The probability that the fourth sock removed is gray is
 .
10 5