Probability MCQs

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1-A certain consulting firm employs 8 men and 4 women. In March, 3 employees are selected
at random to represent the company at a convention. What is the probability that the
representatives will NOT all be men?
A. 14/55
B. 3/8
C. 41/55
D. 2/3
E. 54/55

2-Jeffrey has a bag of marbles. The bag contains 6 red, 6 yellow, 12 green, and 12 blue marbles.
It contains no other marbles.
What is the probability that a marble chosen at random will be either red or yellow?
A. 1/6 B. 1/3 C. 1/2 D. 2/3 E. 3/4

3-A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and 3 different
pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3
days, what is the probability that he wears the same pair of shoes each day, but that no other
piece of clothing is repeated?
(1)(1/3)pow6(1/2)pow3
(2)(1/3)pow6(1/2)
(3)(1/3)pow4
(4)(1/3)pow2(1/2)
(5)5X(1/3)pow2
N.B: pow = power

4-A man is known to speak truth 3 out of 4 times. He throws die and reports that it is a 6. The
probability that it is actually a 6 is
A) 3/4
B) 5/8
C) 2/5
D) 3/5
E) 4/5

5-If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B,
C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of
4-letter code words?
A) 5 to 4
B) 3 to 2
C) 2 to 1 D) 5 to 1
E) 6 to 1

6-From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the
probability that equal numbers of boys and girls will be selected?
A. 1/10
B. 4/9
C. 1/2
D. 3/5
E. 2/3

7-If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the
probability that n(n + 1)(n+2) will be divisible by 8?
A. 1/4
B. 3/8
C. 1/2
D. 5/8
E. 3/4

8-A certain junior class has 1000 students and a certain senior class has 800 students. Among
these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If 1 student is
to be selected at random from each class, what is the probability that the 2 students selected will
be a sibling pair?
a) 3/40,000
b) 3/20,000
c) 1/32
d) 1/20,000
e) None of these

9-A string of 10 lightbulbs is wired in such a way that if any individual lightbulb fails, the entire
string fails. If for each individual lightbulb the probability of failing during time period T id 0.06,
what is the probability that the string of lightbulbs will fail during time period T?
A.0.06
B.(0.06)^10
C.1-(0.06)^10 D.(0.94)^10
E.1-(0.94)^10

10-At a certain business school, 400 students are members of the sailing club, the wine club, or
both. If 200 students are members of the wine club and 50 students are members of both clubs,
what is the probability that a student chosen at random is a member of the sailing club?
A. 1/2
B. 5/8
C. 1/4
D. 3/8
E. 3/5

11-A fair, six-sided die is rolled. What is the probability of obtaining a 3 or an odd number?
A. 1/6
B. 1/5
C. 1/4
D. 2/3
E. 1/2

12-On Saturday morning, Malachi will begin a camping vacation and I will return home at the
end of the first day on Which it rains. If on the first three days of the vacation the probability of
rain on each day is 0.2, what is the probability that Malachi will return home at the end of the
day on the following Monday?
A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

13-Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then
put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the
sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is
numbered 5 ?
A. 1/6
B. 1/5
C. 1/3 D. 2/5
E. 2/3

14-When tossed, a certain coin has equal probability of landing on either side. If the coin is
tossed 3 times, what is the probability that it will land on the same side each time?A.1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2

15-A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2 television
sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2
sets chosen will be a black-and-white set?
A. 1/7
B. 1/4
C. 5/14
D. 11/28
E. 13/26

16-If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the
probability that n(n + 1)(n + 2) will be divisible by 8?
A) 1/4
B) 3/8
C) 1/2
D) 5/8
E) 3/4

17-A bag contains 15 tickets, number from 1 to 15. A ticket is drawn and then another ticket is
drawn without replacement. Find the probability that tickets will show even numbers.
A) 1/5
B) 3/5
C) 4/5 D) 13/20
E) 2/5

18-2 people are to be selected from 10 people, which include male and female. Is the probability
that both them female greater than 1/2?
1) The number of females is greater than 5
2) The probability that both them are male is less than 1/10
A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question
asked.
B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question
asked.
C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is
sufficient alone.
D) Each statement alone is sufficient to answer the question.
E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is
needed to answer the statements.

19-A spider eats 3 flies a day. Until the spider fill its quota, a fly has 50% chance of survival if it
attempts to pass the web. Assuming 5 flies have already made the attempt to pass, what is the
probability that the 6th fly will survive the attempt.
a) 0 %
b) 25 %
c) 50%
d) 75%
e) 100%

20-A total of 9 women and 12 men reside in the 21 apartments that are in a certain apartment
building, one person to each apartment. If a poll taker is to select one of the apartments at random, what is the probability that the resident of the apartment selected will be a woman who
is a student?
(1) Of the women, 4 are students.
(2) Of the women, 5 are not students.
A`. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


Hints/Answers

1. [12C3-8C3]/12C3]
2. 1/3
3.(1/3)^6(1/2)^3
4. 3/4
5. 10P5:10P4 = 6:1
6. [3C2*3C2]/6C4
7. 3/8
8. 60/8,00000
9. (0.94)^10
10. 250/400
11. 1/2
12 .8*.8*.2
13 2/36
14 (1/2)^3
15. 13/28
16. 3/8
17. 1/2
18. try yourself
19. 50%
20. Try yourself