Probability and Statistics
1. If a pair of fair dice is tossed, what is the probability that the sum of the two numbers is 4?
(A)
(B)
(C)
(D)
(E)
2. If a bag contains 5 green marbles and 5 yellow marbles, what is the probability that two marbles
drawn at random are both yellow?
(A)
(B)
(C)
(D)
(E) 1
3. Jim has a bag containing 24 coins. If 10 of the coins are nickels and 8 of the coins are dimes,
what percent are neither nickels nor dimes?
(A) 6%
(B) 10%
(C) 24%
(D) 25%
(E) 30%
4. If a pair of fair dice is tossed, what is the probability that the sum of the two numbers is an even
number less than 10?
(A)
(B)
(C)
(D)
(E)
5. There are 260 people in a room. Twenty percent of them are female. How many of them are
male?
(A) 52
(B) 80
(C) 120
(D) 208
(E) 240
Answers and Explanations
1. The correct answer is C. Each die has 6 possible numbers, therefore there are 36 (
possible rolls or outcomes. The rolls are independent (one does not affect the other). We want to
know how many of these outcomes would add up to 4. We can list out the options and add them
up:
SUM
4
4
4
ROLL 1
1
3
2
ROLL 2
3
1
2
There are 3 of them that meet the desired criteria, so the probability is
2. The correct answer is B. Right away you can eliminate choice E (1) as a probability of one
means that the desired event, in this case drawing 2 yellow marbles at random from a bag
containing green and yellow marbles, has a 100% probability of occurring. Since it’s possible that
it won’t happen, choice E cannot be the answer. To determine the probability, we must look at the
probability of the first marble drawn being yellow. Since 5 out of 10 of the marbles are yellow,
the probability is or . The probability of the second marble being yellow is less since now
there are only 4 yellow marbles left out of 9 marbles total, or . To find the probability of both
marbles being yellow, you multiply the two individual probabilities together:
.
3. The correct answer is D. If there are 24 coins total and 18 (10 + 8) are nickels or dimes, than the
remaining 6 are something else.
4. The correct answer is D. Each die has 6 possible numbers, therefore there are 36 (
possible rolls or outcomes. The rolls are independent (one does not affect the other). We want to
know how many of these outcomes would add up to an even number less than 10, or 2, 4, 6 or 8.
We can list out the options:
SUM
2
4
4
4
6
6
6
6
6
8
8
8
8
8
ROLL 1
1
1
3
2
1
5
2
4
3
2
6
3
5
4
ROLL 2
1
3
1
2
5
1
4
2
3
6
2
5
3
4
There are 14 of them that meet the desired criteria, so the probability is
.
5. The correct answer is D. Of the 260 people in the room, we know that 20% are female. That
means that there are 52 women. If there are 52 females, then that must mean that
are
male. Hence, the correct answer is choice D- 208. Notice that they are asking for the number that
are male, not the percentage (thoughtfully included as choice B). Also included in the answer
choices is the number of females in the room (aka choice A). Don’t be thrown off by those
tricks! Read carefully to ensure you know what each question is really asking!