Multiplying Probabilities
What is the probability of rolling an even number on a standard die and flipping a head on a coin?
(10 seconds)
1/4
You want to order a burger. There are 8 toppings to choose from and you want 2. What’s the probability that you select ketchup and mustard?
(10 seconds)
1/28
Your chocolate milk expired. You need new milk that won’t expire soon. The store has 8 kinds of milk, 3 of which won’t expire soon. How many ways can you choose one milk carton that won’t expire soon?
(10 seconds)
3
There are 20 animals on an alien farm. 4 of these animals are crocodile rabbits and 11 of them are only rabbits. If 3 animals are neither crocodiles or rabbits, how many animals are only crocodiles.
(15 seconds)
8
2 distinct numbers are chosen from the first 7 natural numbers. What is the probability that the greatest common factor of the two numbers is 1?
(30 seconds)
17/21
Twenty tiles are numbered 1 through 20 and are placed into box A. Twenty other tiles numbered 11 through 30 are placed into box B. One tile is randomly drawn from each box. What is the probability that the tile from box A is less than 15 and the tile from box B is either even or greater than 25? Express your answer as a common fraction.
(30 seconds)
21/50
There are 20 students. Half are normal and half aren’t. If you select a group of 3 students from the class, what’s the probability that they’re all not normal?
(15 seconds)
2/19
You have 10 fruits, including an apple and a banana. How many groups of 3 fruit can you have if the group must contain an apple, a banana, or both?
(20 seconds)
64
There 30 students in a grade at a school. All of these students either like math, science, or both. If 4 students love both math and science, and the number of students who like science is 2 times larger than the number of students who like math, how many students have math as their favorite subject.
(20 seconds)
14
Mosely flips 10 fair coins. What is the probability that he obtains more heads than tails or more tails than heads?
(45 seconds)
193/256
Four cards are chosen from a standard 52-card deck, with replacement, what is the probability that it will end up with one card from each suit?
(30 seconds)
3/32
You have 2 decks of 52 cards. What’s the probability that you select 3 numerical cards (2-10) from one deck and 2 aces from the other deck (calculator permitted)?
(60 seconds)
4960/146523
In the “state” of “Wyoming,” license plates have seven letters followed by 2 numbers. If letters 3, 4, and 5 are the same letter, and letters 1 and 7 are the same letter, and numbers can be repeated (e.g. AWOOOGA-11), how many different license plates can you make if the plate can’t have the word “AWOOOGA” on it (calculator permitted)?
(45 seconds)
35879900
A presidential candidate gets 1,254 votes one year. If 999 of these voters are neither republican or democrat, how many voters are either republican, democrat, or both.
(15 seconds)
255
A deck of forty cards consists of four 1's, four 2's,..., and four 10's. A matching pair (two cards with the same number) is removed from the deck. Given that these cards are not returned to the deck, let m/n be the probability that two randomly selected cards also form a pair, where m and n are relatively prime positive integers. Find m/n.
(120 seconds)
55/703
Bag A has 3 white marbles and 4 black marbles. Bag B has 6 yellow marbles and 4 blue marbles. Bag C has 2 yellow marbles and 5 blue marbles. A marble is drawn at random from Bag A. If it is white, a marble is drawn at random from Bag B, otherwise, if it is black, a marble is drawn at random from Bag C. What is the probability that the second marble drawn is yellow?
(40 seconds)
103/245
You really like cows. I mean, you worship them. Their silky, leathery skin and wide soulless eyes are both things that you truly adore. However, some cows are born without one or both of these traits (unimportant how many traits they don’t have, just that they’re missing traits). One day, you decide to buy 10 cows from a farm of 30 cows, with ⅓ of them missing one or both traits. What’s the probability that 3 or fewer of the cows you buy are missing traits (calculator permitted)?
(75 seconds)
16/2731365
There are 15 robins. 8 of them have participated in previous round-robin games. How many ways can you pick 6 robins to compete so that 3 or fewer of the previous participants are competing?
(60 seconds)
3115
100 children were surveyed on their favorite ice cream color out of 3 options: vanilla, chocolate, strawberry. 30 children stated that they like strawberry shortcake. If 10 children said that they liked all 3 equally, and 10 liked just vanilla, 10 liked just chocolate, and 10 liked just strawberry, then what is the sum of the children who liked strawberry and vanilla but not chocolate, strawberry and chocolate but not vanilla, and vanilla and chocolate but not strawberry?
(45 seconds)
45
An urn contains 4 green balls and 6 blue balls. A second urn contains 16 green balls and N blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is 0.58. Find N.
(180 seconds)
144
When three standard dice are tossed, the numbers A, B, C are obtained. Find the probability that (A-1)(B-1)(C-1) does not equal 0.
(45 seconds)
125/216
You have 4 decks of 52 cards, and you want to pick 2 cards from each deck. What is the probability that from each deck, both cards you pick are from the same suit AND you have cards from each suit (calculator permitted)?
(90 seconds)
24/83521
You want to choose a 50-mer from a 400-long DNA sequence with 4 equally-long segments of A, C, G, and T (e.g. AACCGGTT or AAACCCGGGTTT, always in the order of A then C then G then T). How many 50-mers can you choose if exactly half of the 50-mer must contain one letter (e.g. AACC from AACCGGTT)?
(90 seconds)
150
There are 1000 bees in a bee house. 400 bees have sharp stingers. 550 bees have enhanced wings. 475 bees have no legs. 225 bees have both sharp stingers and enhanced wings. 155 have both enhanced wings and no legs. 175 have both no legs and sharp stingers. If every bee has one of these 3 traits, how many bees have all 3?
(45 seconds)
Jenny has 2 red, 2 green, and 2 blue lamps. She arranges them in a row on a table, then turns 3 of them on at random. What is the probability that the leftmost lamp shares its color with the leftmost illuminated lamp?
(210 seconds)
119/600