Addition (Mutually Exclusive)
What is the formula for mutually exclusive events?
P(A or B)= A+B
True or False.
If π΄ and π΅ are events with π(π΄) =0.4, π(π΅) =0.6, and π(π΄ and π΅) =0.24, π΄ and π΅ independent.
True
What is 5!
5*4*3*2*1
120
n!/(n-r)!r!
Write the formula for a permutation (not identical objects)
n!/(n-r)!
A 12-sided die is rolled.
The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Find πβ‘(Less than 5). Simplify.
1/3
A recent poll found that 30% of people think the world is square. If three people are selected at random, what is the probability that all three think the world is square?
.027 or 2.7%
At Taco bell you can get a taco with 2 types of shells, 3 types of meats, and 5 types of toppings. How many different combinations of food could you make.
2 x 3 x 5
30
A bookcase contains 2 travel books and 5 true crime books. If 2 books are chosen at random, the chance that both are travel books is. Write as a fraction.
1/21
7P3
210
If πβ‘(π΄) =0.49, πβ‘(π΅) =0.32, Find πβ‘(π΄ πβ’π π΅) if mutually exclusive.
.81
12 cats and 8 dogs are taken to a zoo. If half of the cats are secretly aliens and 2 of the dogs are aliens, find the probability that an alien is a dog. Write as a fraction.
1/4
When a dice is rolled twice there are how many possible outcomes?
36
Three seniors and seven juniors are available to compete in the hunger games. (They are selecting two students). If each student has an equal chance of being selected, what is the probability that both are seniors? Write as a fraction.
3/45
The numbers 1 through 8 are written in separate slips of paper, and the slips are placed into a coconut. Then, 4 of these slips are drawn at random. What is the probability that the drawn slips are "1", "2", "3", and "4", in that order? Write as a fraction.
nPr = 8!/ (8-4)! = 1680
So 1/1680
Let πΈ be the event of flesh eating bacteria and let π΅ be the event of spontaneous combustion.
Suppose that πβ‘(πΈ) =0.18, πβ‘(π΅) =0.11, and πβ‘(πΈ πβ’πβ’π π΅) =0.06
Find the probability that you will die from either a flesh eating virus, spontaneous combustion, or both at the same time.
P(E or B)=.18+.11-.06
.23
On an four-question true-false quiz, a student guesses each answer. What is the probability that the student gets at least one of the answers correct? Write as a fraction.
.5 x .5 x .5 x .5= (1/16)
1-(1/16)
=(15/16)
There are 4 different mathematics courses, 5 different science courses, and 3 different history courses. If a student must take one of each, how many different ways can this be done?
60
If 40 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets.
1/780
There are 4 different mathematics courses, 5 different science courses, and 3 different history courses. If a student must take one of each and in a certain order, how many different ways can this be done?
1320
Two dice are rolled. Find the probability of getting doubles or a sum of 2. Write as a fraction.
P(doubles or 2)= (6/36)+(1/36)-(1/36)
1/6
A pin of 1000 chickens contains 200 that are "defective". Two chickens are drawn at random and tested. Let A be the event that the first chicken is defective, and let B be the event that the second chicken drawn is defective.
Find πβ‘(π΄ πβ’πβ’π π΅). Write as a decimal with at least four numbers.
P(A and B)= P(A)*P(B|A)
200/1000 * 199/999
39800/999000
.0398
A lottery game called Pick 4 is played by picking four digits, 0 through 9. How many sets of 4 digits are possible if digits cannot be repeated?
10*9*8*7
5040
A package contains 10 batteries, 2 of which are defective. If 3 are selected, find the probability of getting 1 defective battery.
10C3 10*9*8/3*2*1=120
2C1 = 2
8C2 = 28
2*28= 56
56/120 or .4667
On a TV game show, a contestant is shown 11 products from a grocery store and is asked to choose the three least-expensive items in the set, and then correctly arrange these three items in order of price. In how many ways can the contestant choose the three items?
990