MATH 110 Exam 3 Real Practice Questions
(2026) | Verified Answers | A+
• permutation -✓✓An arrangement, or listing, of objects in which order is important.
• p(n,k) -✓✓n! / (n-k)!
• p(n,0) -✓✓1
• combination -✓✓A collection of things, in which the order does not matter.
• c(n,k) -✓✓n! / (k!)(n-k)!
• probability formula -✓✓Favorable Outcomes/Total Possible Outcomes
• odds in favor -✓✓# of favorable outcomes / # of unfavorable outcomes
• odds against -✓✓# of unfavorable outcomes/ # of favorable outcomes
• if A or B are mutually exclusive -✓✓p(A or B) = p(A) + p(B)
• if A and B overlap -✓✓p(A or B) = p(A) + p(B) - p(A and B)
• A magician shuffles a standard deck of playing cards and allows an audience member
to pull out a card, look at it, and replace it in the deck. Four additional people do the
same. Find the probability that of the 5 cards drawn, at least 1 is a face card. (Round
your answer to one decimal place.) -✓✓73.1
• This exercise refers to a standard deck of playing cards. Assume that 5 cards are
randomly chosen from the deck.How many hands contain exactly two 2s and two 8s? -
✓✓1584
• If a person draws three cards from a standard deck (without replacing them), what is
the probability that at least one of the cards is a face card? (Round your answer to one
decimal place.) % -✓✓3= 55.3
4 = 66.2
• If a player bets $5 on the Casino logo denomination, find the player's expectation.
(Round your answer to two decimal places.) -✓✓-1.20= 5
-.96 = 4
- .72 = 3
- .37 = 2
(2026) | Verified Answers | A+
• permutation -✓✓An arrangement, or listing, of objects in which order is important.
• p(n,k) -✓✓n! / (n-k)!
• p(n,0) -✓✓1
• combination -✓✓A collection of things, in which the order does not matter.
• c(n,k) -✓✓n! / (k!)(n-k)!
• probability formula -✓✓Favorable Outcomes/Total Possible Outcomes
• odds in favor -✓✓# of favorable outcomes / # of unfavorable outcomes
• odds against -✓✓# of unfavorable outcomes/ # of favorable outcomes
• if A or B are mutually exclusive -✓✓p(A or B) = p(A) + p(B)
• if A and B overlap -✓✓p(A or B) = p(A) + p(B) - p(A and B)
• A magician shuffles a standard deck of playing cards and allows an audience member
to pull out a card, look at it, and replace it in the deck. Four additional people do the
same. Find the probability that of the 5 cards drawn, at least 1 is a face card. (Round
your answer to one decimal place.) -✓✓73.1
• This exercise refers to a standard deck of playing cards. Assume that 5 cards are
randomly chosen from the deck.How many hands contain exactly two 2s and two 8s? -
✓✓1584
• If a person draws three cards from a standard deck (without replacing them), what is
the probability that at least one of the cards is a face card? (Round your answer to one
decimal place.) % -✓✓3= 55.3
4 = 66.2
• If a player bets $5 on the Casino logo denomination, find the player's expectation.
(Round your answer to two decimal places.) -✓✓-1.20= 5
-.96 = 4
- .72 = 3
- .37 = 2
