Show:
Basic Probability
Permutations
Combinations
Probability on Steroids
Surprise Me!
100
Bruce is going to call one person from his contacts at random. He has 25 total contacts. 20 of those contacts are from his neighborhood. What is the probability that he calls a person NOT from his neighborhood?
5/25 = 0.2
100
A coin is tossed 5 times. Find out the number of possible outcomes. (HTTTT and THTTT are different outcomes)
2^5 = 32
100
You won a free trip to California and can take 2 friends with you. You have 6 friends who want to go. How many different groups of friends could you take with you?
15. (6 choose 2) = 6 * 5 / 2
100
A fair 6-sided die is tossed twice. Find the probability of getting a 4 or 5 on the first toss and a 1, 2, or 3 in the second toss.
1/3 * 1/2 = 1/6
100
If A and B are mutually exclusive events, what is P(A or B)?
P(A) + P(B)
200
If I roll a fair 6-sided die, what is the probability that I roll an odd number? (Odd means NOT divisible by 2)
P(odd) = 3/6 = 1/2
200
How many 3 letter words can we make with the letters in the word 'LOVER'?
5 * 4 * 3 = 60
200
A lottery ticket consists of six numbers, each with a possibility of being from 1 to 49. How many lottery tickets must be purchased to complete all possible combinations of six numbers? (Answer in terms of '!')
(49 choose 6) = 49!/(6!*43!)
200
The probability of obtaining zero defectives in a sample of 40 items is 0.34, while the probability of obtaining 1 defective item in the sample is 0.46. What is the probability of obtaining NOT MORE than 1 defective item in a sample?
0.34 + 0.46 = 0.8
200
There is a party tonight. If my crush goes to the party, then there is a 90% chance that I will go too. If my crush doesn’t go to the party, then there is only a 50% chance that I will go. I find out that there is a 40% chance that my crush will go to the party tonight. Now what is the probability that I will go?
66%. 0.4 * 0.9 + 0.6 * 0.5 = .36 + .3 = .66
300
A standard deck contains 52 cards. If a card is flipped over, what is the probability that it is a a face card (J, Q, K) of any suit?
12/52 = 3/13
300
I am at a restaurant and looking at the menu. There are 5 appetizers, 6 main dishes, and 4 different desserts. If I want to order 1 appetizer, 1 main dish, and 1 dessert, how many different ways can I do this?
5 * 6 * 4 = 120
300
A poker hand consists of 5 cards from a 52 card deck. How many different poker hands are possible? (You can have '!' in your answer)
52 choose 5 = 52!/(5!*47!)
300
The probability that a student passes math is 2/3 and the probability that he passes English is 4/9. If the probability that he will pass at least one subject is 4/5, what is the probability that he will pass both subjects?
(2/3) + (4/9) - (4/5) = 14/45
300
Consider the expansion of (x + y)^10. What is the coefficient of x^3*y^7? You can include '!' in your answer.
(10 choose 3) = 10!/(3!7!)
400
I flip 3 fair coins. What is the probability that I get exactly 2 tails?
3/8
400
How many 7-digit phone numbers can be made under the following conditions: a) The first two digits are '36'. b) The third digit is even (divisible by 2). c) The fourth digit is greater than 5. d) The fifth and sixth digits can be any digit. e) The seventh digit is odd (NOT divisible by 2).
5 * 4 * 10 * 10 * 5 = 10000
400
You are in a small class of 5 girls and 6 boys. A TV show cast comes by and tells you that they are going to pick 3 girls and 3 boys to be on an episode of their TV show. How many different groups of girls and boys can they pick?
200. --- (5 choose 3) * (6 choose 3) = 5!/(3!2!) * 6!/(3!3!) = 10 * 20
400
What is the probability that the total of two dice will be greater than 8, given that the first die is a 6?
2/3
400
How many EVEN (divisible by 2) five-digit numbers can be formed with the digits 1, 2 and 3?
3^4
500
I roll two 6-sided dice. What is the probability that the sum is between 6 and 8?
(5 + 6 + 5) / 36 = 16/36 = 4/9
500
In how many ways can the letters of the word 'LEADER' be arranged?
6!/2! = 360
500
From a group of 7 singers and 6 drummers, 5 people will be selected to form a band. There must be at least 3 singers in the band. How many ways the band member groups be selected?
756. ([5 singers] or [4 singers 1 drummer] or [3 singers 2 drummers])
500
Suppose that you are worried that you might have a rare disease. You decide to get tested, and suppose that the testing methods for this disease are correct 99 percent of the time (in other words, if you have the disease, it shows that you do with 99 percent probability, and if you don't have the disease, it shows that you do not with 99 percent probability). Suppose this disease is actually quite rare, occurring randomly in the general population in only one of every 10,000 people. If your test results come back positive, what are your chances that you actually have the disease?
P(disease | positive) = .01 = 1%
500
How many numbers between 1 and 100 (inclusive) are divisible by 3 or 10?
40. (43 - 3)