Random Math
5!/3!
20
Can -0.53 be the probability of an outcome in a sample space? Explain.
No, probability can't be a negative.
Calculate the combination
6C2
15
Calculate the permutation:
3P2=
6
A coin is tossed 3 times, how many possible outcomes are there?
2 * 2 * 2 = 8
What are the possible outcomes for flipping a coin two times?
HH
HT
TH
TT
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 2". Find P(A).
Outcome Probability
1 0.1
2 0.2
3 0.7
0.1
There are 5 math books and 11 statistics books. 5 books are randomly selected. What the total number of ways to select the books?
Write your answer as a numeric answer.
16 choose 5 = 4368
How many unique ways are there to arrange the letters in the word SONG?
4! = 24
Ariel is planning a workout. She needs to choose one of the 4 cardio routines and one of the 2 resistance training routines. For the time of day, Ariel has 4 options that work with her schedule. How many different workouts can Ariel plan?
4*4*2 = 32
A card is drawn at random from a standard deck. What is the probability that card is the “5 of clubs”?
1/52 = 0.01923
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is greater than or equal to 3, or less than or equal to 1". Find P(A).
Outcome Probability
0 0.1
1 0.2
2 0.3
3 0.3
4 0.1
0.4 + 0.3 = 0.7
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A. 24400
B. 21300
C. 210
D. 25200
D.
You have 6 reindeer, Ruby, Red, Rose, Rain, Ramen, and Rob and you want to have 5 fly your sleigh. You want to have your reindeer in a single file line
How many different ways can you arrange the reindeer in a line?
6! = 720
In an experiment, the probability that event A occurs is 3/8 and the probability that event B occurs is 3/7.If A and B are independent events, what is the probability that A and B both occur?Simplify any fractions.
P(A and B) = P(A)P(B)
= (3/8)(3/7)
= 9/56
In how many ways can 5 man draw water from 5 taps if no tap can be used more than once?
A. None of these
B. 720
C. 60
D. 120
5! = 5*4*3*2*1 = 120
In an experiment, the probability that event A occurs is 6/7 and the probability that event B occurs is 4/9.If A and B are independent events, what is the probability that A and B both occur?Simplify any fractions.
P(A and B) = P(A)P(B)
= (6/7)(4/9)
= 8/21
Are the following 4 equations true or false?
A) 10C2 = 10C8
B) 6C1 = 6C5
C) 8C2 = 8C4
D) 100C30 = 100C70
B) true
C) false
D) true
For any xCy, xCy = xCx-y
How many different ways can you arrange the word “loose"?
Hint: We need to account for there being 2 O’s.
5!/2! = 60
Michael is filling out summer job applications, so that he can earn money to buy a car. Of the 8 jobs he's applying for, 6 are construction jobs.
If Michael randomly picks 5 applications to submit today, what is the probability that all of them are for construction jobs?
Write your answer as a decimal rounded to four decimal places.
6/56 or 0.1071
total # of outcomes = 8 Choose 5 = 56
total # of outcomes in the event = 6 choose 5 = 6
A card is randomly drawn from a deck. Find the probability that the card is not an ace.
Simplify your answer.
48/52 = 12/13
In an experiment, the probability that event A occurs is 4/9, the probability that event B occurs is 6/7, and the probability that events A and B both occur is 2/5.What is the probability that A occurs given that B occurs? Simplify any fractions.
P(A|B) = P(A and B)
P(B)
= 2/5 = 7/15 = 0.46666….
6/7
Jasmine and Mathis made a list of 8 psychology experiments they want to try at home. Each experiment tackles one specific psychology topic. 5 of the experiments involve yawning.
If Jasmine and Mathis randomly choose 4 experiments to try over the summer, what is the probability that all of them involve yawning?
Write your answer as a decimal rounded to four decimal places.
5/70 = 0.0714
total outcomes = 70
# of outcomes in an event = 5
How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
Give your answer as a numeric answer.
10P3 = 720
There are 10 unique letters and the order of letters matters.
In an experiment, the probability that event A occurs is 3/8, the probability that event B occurs is 2/3, and the probability that events A and B both occur is 1/6. What is the probability that A occurs given that B occurs? Simplify any fractions.
P(A|B) = P(A and B)
P(B)
= 1/6 = 1/4
2/3