PROBABILITY AND STATISTICAL INFERENCE
ACTUAL EXAM PAPER 2026 QUESTIONS WITH
SOLUTIONS GRADED A+
◉ 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. Answer: (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.
Answer: Combinations: 5 people, 3 males (4N3)(6N2)/(10N5)
◉ T or F: if P(A intersect B) = 0 then A and B are mutually exclusive.
Answer: 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):. Answer: {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}:
,What is P(A intersect B):. Answer: {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). Answer: {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). Answer: 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. Answer: 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):. Answer: (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:. Answer: NP =
3.6
◉ IF the number of spelling errors per page is know to be Poisson(2),
then:
What is the probability that there are no mistakes on one page:. Answer:
e^-2 * 2^! = .135
◉ IF the number of spelling errors per page is know to be Poisson(2),
then:
What is the probability that there are at least 2 mistakes on 3 pages.
Answer: SO inf E x=2 (e^-6 * 6^x) / X!
◉ What is the mean of the following distribution:
ACTUAL EXAM PAPER 2026 QUESTIONS WITH
SOLUTIONS GRADED A+
◉ 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. Answer: (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.
Answer: Combinations: 5 people, 3 males (4N3)(6N2)/(10N5)
◉ T or F: if P(A intersect B) = 0 then A and B are mutually exclusive.
Answer: 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):. Answer: {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}:
,What is P(A intersect B):. Answer: {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). Answer: {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). Answer: 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. Answer: 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):. Answer: (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:. Answer: NP =
3.6
◉ IF the number of spelling errors per page is know to be Poisson(2),
then:
What is the probability that there are no mistakes on one page:. Answer:
e^-2 * 2^! = .135
◉ IF the number of spelling errors per page is know to be Poisson(2),
then:
What is the probability that there are at least 2 mistakes on 3 pages.
Answer: SO inf E x=2 (e^-6 * 6^x) / X!
◉ What is the mean of the following distribution:
