Show:
Disjoint Events
Overlapping Events
Independent Events
Dependent Events
Identify the type of Events
100
To find the probability of disjoint events you ______ P(A) and p(B)
What is add? P(A or B)=P(A)+P(B)
100
To find the probability of overlapping events, you must ________ the probability that the events occur at the same time.
What is subtract? P(A or B)=P(A)+P(B) - P(A and B)
100
To find the probability of independent events, __________ P(A) and P(B)
What is multiply? P(A and B)= P(A) x P(B)
100
To find the probability of dependent events, multiply P(A) by the P(B, ______ A).
What is given? P(A and B)= P(A) x P(B, given A)
100
Determine if the following are disjoint or overlapping Event A: A person knows how to ski Event B: A person does not know how to ski
What is disjoint? You cannot both know how and not know how to ski
200
Event A and B are disjoint. P(A)=3/25, P(B)=16/25 Find P(A or B).
What is 19/25 ? 3/25+16/25=19/25
200
Event A and B are overlapping P(A)=11/25, P(B)=7/25 P(A and B)=3/25
What is 3/5 ? 11/25+ 7/25 - 3/25 = 15/25 = 3/5
200
You roll a die and flip a coin. Find P(odd and heads).
What is 1/4? P(odd and heads)= 3/6 x 1/2 = 3/12= 1/4
200
You write each letter of the word F-E-B-R-U-A-R-Y on a slip of paper and place them in a hat. You draw a slips and WITHOUT REPLACING it draw a second slip. Find P(F, R). Write your answer as a fraction in simplest form.
What is 1/28? P(F, R) = P(F) x P(R, given F)= 1/8 x 2/7=2/56
200
Determine if the following events are Independent or Dependent Event A: Roll a Number Cube Event B: Roll a 2nd number Cube
What is independent? Rolling the first cube has no affect on the outcomes on the second cube
300
Events A and B are disjoint. P(A)=12/50, P(B)=21/50. Find P(A or B).
What is 33/50? 12/50+21/50=33/50
300
Event A and B are overlapping P(A)=16%, P(B)=15% P(A and B)=7% Find P(A or B)
What is 24% 16+15 - 7= 24
300
You roll a number cube twice. Find P(5, then 6) Write your answer as a fraction.
What is 1/36? P(5, then 6) =1/6 x 1/6
300
You made 3 vanilla, 3 chocolate and 4 strawberry cupcakes. You randomly hand them out to your classmates. Find the probability that the first two cupcakes you hand out are vanilla and chocolate.
What is 1/10? P(vanilla, chooclate)= P(vanilla) x P(chocolate, given vanilla) 3/10 x 3/9=9/90=1/10
300
Determine if the events are independent or dependent. You buy two gumballs from a machine.
What is dependent? You cannot put the first gumball back into the machine, thus changing the possible outcomes for the second gumball.
400
Sam asked his classmate their favorite food. The results are 8--pizza 12--hamburgers 14--pasta 6--steak If Sam chooses a random student, find the probability that his/her favorite food is pizza or steak? Write your answer as a fraction in simplest form.
What is 7/20? 8/40+6/40=14/40
400
A survey found that in a town, 24% of the population owned dogs, 15% of the population owned cats and 4% of the population owned both a cat and dog. Find the probability that a randomly chosen citizen of the town owns a cat or dog.
What is 35% P(Cat or Dog)=15+24 - 4
400
You roll a 6-sided die two times and flip a coin. Find P(3, a # less than 4, tails) Write your answer as a fraction in simplest form
What is 1/24? P(3, # less than 4, tails)= 1/6 x 3/6 x 1/2 = 3/72
400
There are 12 girls and 13 boys in a chorus. Two students will be randomly chosen to sing a solo in the upcoming concert. Find the probability that two girls are chosen to sing the solos.
What is 11/50 ? P(girl, girl)= P(girl) x P(girl, given girl) 12/25 x 11/24= 132/600=11/50
400
Determine if the events are disjoint, overlapping, independent or dependent. In a science class there are 10 boys and 8 girls. The teacher randomly selects 2 students to present their projects.
What is dependent? Both students will eventually present (compound event), but once the first student is chosen they will not part of the possible outcomes when the teacher picks the second presenter.
500
Carly picks a card from a standard deck. Find P(Face card or 3). Write your answer as a fraction in simplest form *note Face cards are Jack, Queen and King
What is 4/13? 12/52+4/52=16/52
500
You pick a card from a standard deck. Find the P(face card or black) *note face cards are Jack, Queen and King Write your answer as a fraction in simplest form
What is 8/13? P(face card or black) = 12/52 + 26/52 - 6/52= 32/52
500
You have a bag with 10 red, 14 yellow and 6 blue marbles. You select a marble, record its color and return it to the bag. You repeat this for a total of 4 trials. Find P(red, red, blue, yellow) Write your answer as a fraction in simplest form.
What is 7/675? P(red, red, blue, yellow) = 10/30 x 10/30 x 6/30 x 14/30
500
You have a standard deck of cards. You pull a card from the deck and do not replace it before drawing another card. You do this until you have 3 cards in your hand. Find the probability that you are holding 2 red cards and one black card. Write your answer as a fraction in simplest form.
What is 13/102? P(red, red, black)= P(red) x P(red, given red) x P(black, given red red) 26/52 x 25/51 x 26/50
500
Determine if the events are disjoint, overlapping, independent or dependent. You roll three number cubes. Find the probability of rolling a 4, an odd and a 3.
What is independent? There are three events (rolling the cube), but the possible outcomes do not change from one event to the next.