PROBABILITY AND STATISTICAL
INFERENCE EXAM QUESTIONS AND
CORRECT ANSWERS. VERIFIED
2025/2026.
From a group of 10 people, 4 males and 6 females:
How many ways can you line the people up - ANS 10! = 3,628,800
From a group of 10 people, 4 males and 6 females:
How many ways can you the line the people up if you just differentiate by the gender of the
individual - ANS (10N4)(6N6) = 210
From a group of 10 people, 4 males and 6 females:
What is the probability that a committee of size 5 has exactly 3 males - ANS Combinations: 5
people, 3 males (4N3)(6N2)/(10N5)
T or F: if P(A intersect B) = 0 then A and B are mutually exclusive - ANS False, must be the
empty set
You put the letters a,b,c,d,e in a hat and randomly pick one. Let A={a,b,d} and B={d,e}:
What is P(A union B): - ANS {A,B,D,E} so, probability 4/5
3 you put the letters a,b,c,d,e in a hat and randomly pick one. Let A={a,b,d} and B={d,e}:
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
, What is P(A intersect B): - ANS {D} so, probability 1/5
3 you put the letters a,b,c,d,e in a hat and randomly pick one. Let A={a,b,d} and B={d,e}:
What is P(A intersect B compliment) - ANS {A,B} so, probability 2/5
you are give the following facts:
P(A) = 2P(B)
A and B are mutually exclusive
A and B are exhaustive events
What is P(A) - ANS S = A union B because they are exhaustive
P(S) = P(A) + P(B)
P(S) = P(A) + 1/2P(A)
What is the probability of picking 3 queens in a row from a deck of 52 cards. Order is noted and
cards are not replaced - ANS Counting problem. (4*3*2)/(52*51*50)
The probability that a WWU student pulls an all-nighter on a given day is 30%. Let X = the
number of students out of 12 who pull an all-nighter tonight. Assuming that students
"independently" choose to pull all-nighters:
What is P(X=4): - ANS (12CX)(.3^x)(1-.3)^(12-x) = .231
The probability that a WWU student pulls an all-nighter on a given day is 30%. Let X = the
number of students out of 12 who pull an all-nighter tonight. Assuming that students
"independently" choose to pull all-nighters:
What is the expected value of the associated distribution: - ANS NP = 3.6
IF the number of spelling errors per page is know to be Poisson(2), then:
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
INFERENCE EXAM QUESTIONS AND
CORRECT ANSWERS. VERIFIED
2025/2026.
From a group of 10 people, 4 males and 6 females:
How many ways can you line the people up - ANS 10! = 3,628,800
From a group of 10 people, 4 males and 6 females:
How many ways can you the line the people up if you just differentiate by the gender of the
individual - ANS (10N4)(6N6) = 210
From a group of 10 people, 4 males and 6 females:
What is the probability that a committee of size 5 has exactly 3 males - ANS Combinations: 5
people, 3 males (4N3)(6N2)/(10N5)
T or F: if P(A intersect B) = 0 then A and B are mutually exclusive - ANS False, must be the
empty set
You put the letters a,b,c,d,e in a hat and randomly pick one. Let A={a,b,d} and B={d,e}:
What is P(A union B): - ANS {A,B,D,E} so, probability 4/5
3 you put the letters a,b,c,d,e in a hat and randomly pick one. Let A={a,b,d} and B={d,e}:
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
, What is P(A intersect B): - ANS {D} so, probability 1/5
3 you put the letters a,b,c,d,e in a hat and randomly pick one. Let A={a,b,d} and B={d,e}:
What is P(A intersect B compliment) - ANS {A,B} so, probability 2/5
you are give the following facts:
P(A) = 2P(B)
A and B are mutually exclusive
A and B are exhaustive events
What is P(A) - ANS S = A union B because they are exhaustive
P(S) = P(A) + P(B)
P(S) = P(A) + 1/2P(A)
What is the probability of picking 3 queens in a row from a deck of 52 cards. Order is noted and
cards are not replaced - ANS Counting problem. (4*3*2)/(52*51*50)
The probability that a WWU student pulls an all-nighter on a given day is 30%. Let X = the
number of students out of 12 who pull an all-nighter tonight. Assuming that students
"independently" choose to pull all-nighters:
What is P(X=4): - ANS (12CX)(.3^x)(1-.3)^(12-x) = .231
The probability that a WWU student pulls an all-nighter on a given day is 30%. Let X = the
number of students out of 12 who pull an all-nighter tonight. Assuming that students
"independently" choose to pull all-nighters:
What is the expected value of the associated distribution: - ANS NP = 3.6
IF the number of spelling errors per page is know to be Poisson(2), then:
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
