A) Vocabulary
the list of all possible outcomes
What is the sample space?
#2: A survey of 106 households was done to investigate the type of pets in the house. The results are shown in the Venn diagram below. If a household was selected at random, which of the following would be the probability the house would have cats given they don't have dogs?
(See Review document for Venn Diagram)
(1) 0.33
(2) 0.48
(3) 0.56
(4) 0.63
(3) 0.56
There are 63 total households that do not have dogs (35 + 28). Of those, 35 of them have cats. So, the probability is 35/63 = 0.5555... = 0.56
A coin and a die are both rolled. What is the probability of flipping tails and an even number?
What is (1/2 * 1/2 =) 1/4?
#1: In Sean's class there are 13 boys and 16 girls. Sean will randomly pull one of their names out of a hat to give a presentation to the class. Which of the following is the probability the student picked will be a girl?
(1) 0.45 (3) 0.62
(2) 0.55 (4) 0.81
(2) 0.55
n(G)/n(C) = 16/(13+16) = 0.5517.... = 0.55
What is experimental probability?
What is the outcome when an experiment is completed.
A bag contains marbles; 3 red, 2 green, 5 yellow, 8 black, 4 purple. The probability of drawing a yellow marble and then a black marble and is it independent or dependent
5/22 * 8/21 =
What is 20/231 and dependent?
the result of an event
What is the outcome?
A spinner has 6 equal sections, red, blue, yellow, green, orange, and pink. What is the probability that the spinner will land on yellow?
What is 1/6?
A bag contains the following marbles: 4 red, 2 green, 3 yellow, and 1 orange. What is the probability that a green then a red will be picked, if the marble is replaced for the second draw.
What is (2/10 * 4/10 =) 8/100 or 2/25?
# 5: Max has a bowl of 30 grapes, of which 60% of which are red grapes and 40% are white grapes. If he pulls two grapes randomly from the bowl without replacement then which of the following is the probability that they are both red?
(1) 9/25 (3) 51/145
(2) 22/145 (4) 16/25
(3) 51/145
18/30 x 17/29 = 306/870 = 51/145
A boy tosses a coin and gets heads 7 times out of 20. Is this theoretical or experimental?
What is experimental?
Flipping a coin and if it is tails rolling a die for 4 or greater. The probability and whether it is independent or dependent.
1/2 * 1/2 =
What is 1/4 and dependent
what is expected/ predicted to happen in a probability question.
What is theoretical probability?
A spinner has 10 equal sections, 1,2,3,4,5,6,7,8,9, and 10. If the spinner is spun, what is the probabilty of spinning a number less than 7?
What is 6/10 or 3/5?
A drawer contains 4 white, 4 black, 2 yellow, and 5 polka-dot socks and Julie wants to find a pair of yellow socks to wear to school. What is the probability that she will choose a pair of yellow socks in her first two picks if she doesn't replace the sock she draws first.
What is (2/15 * 1/14 =) 2/210 = 1/105?
# 7: If a fair coin is tossed five times, which of the following is closest to the probability that at least one head will be tossed?
(1) 50% (3) 80%
(2) 75% (4) 97%
(4) 97%
P(all tails) = (1/2)^5 = 0.03125
P(at least one head) = 1 - 0.03125 - 0.96875 = 97%
The probability of drawing a face card from a standard deck of cards is 3/13. Is this theoretical or experimental probability?
What is theoretical?
flipping a coin followed by flipping another coin. The probability and independent or dependent.
1/2 * 1/2=
What is 1/4 and independent?
A drawer contains 20 socks: 8 blue, 4 green, 6 black, and 2 white. What is the probability of picking out a blue sock?
What is 8/20 or 2/5?
A blue number cube and an orange number cube are rolled. What is the P(3, then even)?
What is (1/6 * 1/2 =) 1/12?
(the colors are extraneous information)
#3: At a local community college, 56% of all freshmen take both statistics and psychology. What percent of freshmen taking psychology are taking statistics if 62% of freshmen are taking psychology?
(1) 35% (3) 86%
(2) 58% (4) 90%
(4) 90%
P(SlP) = P(S and P)/P(P) = .56/.62 = .9032 = 90%
A heart is randomly chosen from a deck of cards 7 out of 12 times. What is the experimental probability?
What is 7/12?
#4: If two events, A and B, are independent then which of the following is always true about their probabilities?
(1) P(A) = P(B)
(2) P(A given B) = P(A)
(3) P(A or B) = P(A) x P(B)
(4) P(A and B) = P(A)/P(B)
(2) P(A given B) = P(A)
If two events are independent then the probability of one of them happening given the other one has happened doesn't change. This is indicated by choice 2.
If the probability of an event is 0, then the event is this.
Impossible
A class has 20 boys and 12 girls. What is the percent chance that the teacher will choose a girl to answer a question?
What is 12/32 = 37.5%?
A spinner with equal sections of red, blue, green, and purple is spun while a number cube is rolled. What is the P (not blue and not a 3)
What is (3/4 * 5/6 =) 15/24 or 5/8?
#6: The 11th grade class at Red Hook high school was surveyed about the types of music they liked. Of those surveyed, 64% said they liked pop music and 52% said they liked rap music. If 38% said they liked both pop and rap, what percent of those surveyed liked neither?
(1) 22% (3) 31%
(2) 27% (4) 36%
(1) 22%
P (P or R) = P(P) + P(R) - P(P and R)
= 0.64 + 0.52 - 0.38 = .78 or 78%
P(neither) = 1 - 0.78 = 0.22 or 22%
A heart is randomly chosen from a deck of cards 7 out of 12 times. What is the theoretical probability?
What is 1/4?
5 unique bunnies in a bag. The probability that a black bunny will escape once the white and the spotted one have escaped ...and is it independent or dependent.
1/5 * 1/4 * 1/3 =
What is 1/60 and dependent?