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Probability Module – Page 1
Session 12
(C) 1
13. An integer n is to be chosen at random from a set of 5
(D) 2
consecutive integers. Which of the following must be
(E) 3
less than ½ ?
22. If set A is {3, 5, 7, 11, 19} and set B consists of all the
I. The probability that n is even
even numbers between 1 and 11, how many elements
II. The probability that n is odd
are in the union of the two sets?
III. The probability that n is the median of the set
(A) 0
(A) I only
(B) 10
(B) II only
(C) 11
(C) III only
(D) 19
(D) I and II only
(E) 30
(E) II and III only
23. If set X contains 5 distinct elements and set Y contains
18. Joey flips four fair coins in a row. If x is the probability
7 distinct elements, what is the maximum possible
that only the first two coins will come up heads, y is the
number of distinct elements that could be in the
probability that only the last two coins will come up heads,
intersection of the two sets?
and z is the probability that all four coins will come up
heads, then which of the following is true?
(A) 2
(B) 5
(A) x < y < z
(C) 7
(B) x = y < z
(D) 9
(C) x < y = z
(E) 12
(D) x = y = z
(E) x = y > z
24. If set A contains all even integers and set B contains all
numbers between –3 and 3, then which of the
SETS
following statements is true?
19. Set P consists of all the prime numbers among the first
I. 2 is in the intersection of set A and set B.
100 positive integers. Set E consists of all the even
II. –2 is in the intersection of set A and set B.
numbers among the first 100 positive integers. Which
III. –2 is in the union of set A and set B.
of the following must be true?
(A) I only
(B) III only
I. Set P contains more numbers than set E.
(C) I and II only
II. The intersection of the two sets contains exactly
(D) I and III only
one number.
(E) I, II, and III
III. The union of the two sets contains exactly
one number.
SEQUENCES
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
20. If set R contains 10 distinct even integers and set S
contains 10 distinct negative integers, what is the
maximum possible number of elements in the
intersection of the two sets?
(A) 0
(B) 4
(C) 6
(D) 8
(E) 10
21. If set E is {A, B, C, 1, 2, 3} and set I is {1, 3, 5, A,
B, Q}, which of the following elements could be
in the union of the two sets, but not in their
intersection?
(A) A
(B) B
1. In the geometric sequence 4, 12, 36, x, 324, 972, … ,
what is the value of x?
(A) 60
(B) 64
(C) 108
(D) 198
(E) 265
Probability Module – Page 2
–2, 0, 2, 4
3. A sequence is formed by repeating the 4 numbers
above in the same order indefinitely. What is the sum
of the first 32 terms of the sequence?
4. In the sequence 7, 14, 28, x, 112, . . . , what is the
value of x?
(A) 35
(B) 56
(C) 63
(D) 75
(E) 91
5. The first term in a sequence is 5. Every subsequent
term is obtained by adding 3 to the previous term, then
dividing by –1. What is the 142nd term in the
sequence?
(A) –428
(B) –8
(C) 5
(D) 147
(E) 431
Probability Module – Page 3