Probability is usually considered a tricky topic. Many aspirants go out of their way and practice difficult questions pertaining to the topic. But you can be assured that the probability is low that you will get a lot of probability in GRE!
You might encounter some 1-3 questions on probability and usually of easy level of difficulty. The type of probability questions that you might see in GRE range from coin tosses to objects being removed from group without replacement. These can be easily solved with some practice.
So, to save you from spending too much time on the topic, we have posted the concept overview and some practice questions.
PROBABILITY
Probability is a measure of the likelihood of an event to occur. The probability of an event is number between 0 and 1 inclusive, with a probability of 0 meaning “unlikely to happen” and a probability of 1 meaning “guaranteed to happen”. The higher the probability, the higher the chance an event will occur.
An event may
include more than one outcome.
Probability
is calculated as
PROBABILITY OF MULTIPLE
EVENTS
To calculate
the probability of two or more independent events occurring, multiply the
probabilities of the individual events.
To calculate
the probability of two or more dependent events occurring, multiply the individual
probabilities, but the probability of each dependent even must also be
calculated.
P(A
or B) = P(A) + P(B) – P(A and B)
PRACTICE
QUESTIONS:
(1) What is
a probability of rolling a four on three consecutive rolls of a fair six sided
die?
🔘1/216
🔘1/36
🔘1/6
🔘1/15
🔘None of the Above
Answer : 1/216
(2) What is
the probability that two rolls of a fair six-sided die will result in an odd
number?
🔘1/8
🔘1/2
🔘1/5
🔘1/16
🔘1/4
Answer : 1/4
(3)
|
QUANTITY A |
QUANTITY B |
|
What is the probability of the result
of 4 independent coin flips being exactly 1 head and 3 tails? |
1/4 |
🔘Quantity B is greater
🔘Both quantities are equal
🔘
Answer : Both quantities are equal
(4) A bag
contains only yellow and green plastic balls. There were 16 balls in the bag
and 1 green ball was removed. The probability of drawing a green ball was then
1/3. How many yellow balls were in the bag? (Numeric Entry)
(5) A bag
contains only 6 black marbles and 4 white marbles. Jack wants to get a blue
marble from the bag, but he cannot see what colour marble he draws until he takes
it out of the bag. Jack will stop drawing marbles as soon as he gets a white
one. If Jack does not draw a white marble in 3 attempts, he stops. What is the
probability that he will draw a white marble?
🔘5/6
🔘1/15
🔘3/5
🔘1/6
🔘4/15
Answer : 1/6
(6) Events A
and B are independent, but not mutually exclusive. The probability that event A
occurs is 0.3 and the probability that at least one of the events A or B occurs
is 0.8. What is the probability that event B occurs?
🔘0.28
🔘0.40
🔘0.15
🔘0.67
🔘0.83
Answer : 0.28
(7) A
six-sided die used for a board game has the letter A on 4 sides, B on 1 sides,
and C on the remaining side. What is the probability of rolling an A, a B, and
a C on 3 rolls of the die, in any order?
🔘1/6
🔘1/3
🔘1/9
🔘1/36
🔘1/45
Answer : 1/9
(8) A jar contains 10 red marbles, 4
white marbles, and 2 blue marbles. Two are drawn in sequence, not replacing
after each draw.
| QUANTITY A | QUANTITY B |
| The probability of drawing two red marbles. | The probability of drawing exactly one blue marble. |
🔘Quantity A is greater
🔘Quantity B is greater
🔘Both quantities are equal
🔘The relationship cannot be determined
Answer : Quantity A is greater
(9)Two fair dice
are thrown. What is the probability that the outcome will either total 7 or
include a 3?
🔘2/3
🔘8/9
🔘5/12
🔘1/2
🔘7/12
Answer : 5/12
(10) What is the
probability of drawing 2 hearts from a standard deck of cards without
replacement?
🔘13/52
🔘1/16
🔘12/52
🔘1/4
🔘1/17
Answer : 1/17
(11) There are
four aces in a standard deck of playing cards. What is the approximate probability
of drawing two consecutive aces from a standard deck of 52 playing cards?
🔘0.4
🔘0.5
🔘0.05
🔘0.005
🔘0.004
Answer : 0.005
(12) A 6-sided cube has sides numbered 1 through 6. If the cube is rolled twice, what is the probability that the sum of the two rolls is equal to 8?
🔘1/9
🔘1/8
🔘5/36
🔘1/6
🔘7/36
Answer : 5/36
(13) An integer is randomly chosen from 2 to 20 inclusive.
What is the probability that the number is prime? (Numeric Entry)
Answer : 8/19
(14) A bag contains 6 red chips numbered 1–6 respectively
and 6 blue chips numbered 1–6 respectively. If 2 chips are to be picked
sequentially from the bag of 12 chips, without replacement, what is the
probability of picking a red chip and then a blue chip with the same number? (Numeric Entry)
Answer : 1/22
(15) Bob has a 24-sided die with an integer between 1 and 24
on each face. Every number is featured exactly once. When he rolls, what is the
probability that the number showing is a factor of 24? (Numeric Entry)
Answer : 1/3
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