PROBABILITY AND STATISTICAL INFERENCE — 10TH
EDITION LATEST REAL QUESTIONS AND CORRECT
DETAILED ANSWERS (CORRECT VERIFIED ANSWERS) A
NEW UPDATED VERSION
Section 1: Probability Fundamentals
1. A fair six-sided die is rolled once. What is the probability of obtaining an even
number?
A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{2}\)
D. \(\frac{2}{3}\)
Correct answer: C. \(\frac{1}{2}\)
Rationale: The even outcomes are 2, 4, and 6. Three of the six equally likely
outcomes are even, so the probability is \(3/6=1/2\).
2. If \(P(A)=0.65\), what is \(P(A^c)\)?
,A. 0.35
B. 0.45
C. 0.65
D. 1.65
Correct answer: A. 0.35
Rationale: The complement rule states that \(P(A^c)=1-P(A)=1-0.65=0.35\).
3. Suppose \(P(A)=0.4\), \(P(B)=0.5\), and \(P(A\cap B)=0.2\). Find \(P(A\cup B)\).
A. 0.2
B. 0.5
C. 0.7
D. 0.9
Correct answer: C. 0.7
,Rationale: The addition rule gives \(P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.4+0.5-
0.2=0.7\).
4. Events \(A\) and \(B\) are independent if:
A. \(P(A\cap B)=0\)
B. \(P(A\cap B)=P(A)+P(B)\)
C. \(P(A\mid B)=P(B)\)
D. \(P(A\cap B)=P(A)P(B)\)
Correct answer: D. \(P(A\cap B)=P(A)P(B)\)
Rationale: Independence means that the occurrence of one event does not
change the probability of the other. The product rule characterizes independence.
5. A card is drawn from a standard 52-card deck. What is the probability that it is
a heart?
A. \(\frac{1}{13}\)
B. \(\frac{1}{4}\)
, C. \(\frac{1}{2}\)
D. \(\frac{4}{13}\)
Correct answer: B. \(\frac{1}{4}\)
Rationale: There are 13 hearts among 52 cards, giving \(13/52=1/4\).
6. If \(P(A)=0.7\), \(P(B)=0.4\), and \(A\) and \(B\) are independent, calculate
\(P(A\cap B)\).
A. 0.11
B. 0.28
C. 0.30
D. 0.70
Correct answer: B. 0.28
Rationale: For independent events, \(P(A\cap B)=P(A)P(B)=0.7(0.4)=0.28\).
7. A fair coin is tossed three times. What is the probability of obtaining exactly
two heads?
EDITION LATEST REAL QUESTIONS AND CORRECT
DETAILED ANSWERS (CORRECT VERIFIED ANSWERS) A
NEW UPDATED VERSION
Section 1: Probability Fundamentals
1. A fair six-sided die is rolled once. What is the probability of obtaining an even
number?
A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{2}\)
D. \(\frac{2}{3}\)
Correct answer: C. \(\frac{1}{2}\)
Rationale: The even outcomes are 2, 4, and 6. Three of the six equally likely
outcomes are even, so the probability is \(3/6=1/2\).
2. If \(P(A)=0.65\), what is \(P(A^c)\)?
,A. 0.35
B. 0.45
C. 0.65
D. 1.65
Correct answer: A. 0.35
Rationale: The complement rule states that \(P(A^c)=1-P(A)=1-0.65=0.35\).
3. Suppose \(P(A)=0.4\), \(P(B)=0.5\), and \(P(A\cap B)=0.2\). Find \(P(A\cup B)\).
A. 0.2
B. 0.5
C. 0.7
D. 0.9
Correct answer: C. 0.7
,Rationale: The addition rule gives \(P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.4+0.5-
0.2=0.7\).
4. Events \(A\) and \(B\) are independent if:
A. \(P(A\cap B)=0\)
B. \(P(A\cap B)=P(A)+P(B)\)
C. \(P(A\mid B)=P(B)\)
D. \(P(A\cap B)=P(A)P(B)\)
Correct answer: D. \(P(A\cap B)=P(A)P(B)\)
Rationale: Independence means that the occurrence of one event does not
change the probability of the other. The product rule characterizes independence.
5. A card is drawn from a standard 52-card deck. What is the probability that it is
a heart?
A. \(\frac{1}{13}\)
B. \(\frac{1}{4}\)
, C. \(\frac{1}{2}\)
D. \(\frac{4}{13}\)
Correct answer: B. \(\frac{1}{4}\)
Rationale: There are 13 hearts among 52 cards, giving \(13/52=1/4\).
6. If \(P(A)=0.7\), \(P(B)=0.4\), and \(A\) and \(B\) are independent, calculate
\(P(A\cap B)\).
A. 0.11
B. 0.28
C. 0.30
D. 0.70
Correct answer: B. 0.28
Rationale: For independent events, \(P(A\cap B)=P(A)P(B)=0.7(0.4)=0.28\).
7. A fair coin is tossed three times. What is the probability of obtaining exactly
two heads?
