Simple Probabilities
515 total people were surveyed. 241 of them were male and 274 of them were female. What is the probability that a randomly selected survey participant is female. (round to the nearest tenth)
53.2% are female
What are conditional probabilities?
A conditional probability is the probability that an event will occur, given that a separate event that effects the outcome has taken place as well.
If the probabilities of two events are presented in a Venn diagram, what does the overlapping center part of the Venn diagram represent?
The overlapping center part of the Venn diagram represents the probability of both represented events occurring.
What makes two events mutually exclusive or disjoint?
Two events are mutually exclusive or disjoint if they cannot occur at the same time.
General formula for probability:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
119 people were surveyed. 29 of them were between the ages 18-25, 53 were 26-40, 30 were 41-65, and 7 were 66 and older. What is the probability that a randomly selected survey participant is between the ages 41-65? (round to the nearest tenth)
25.2% are between the ages 41-65
Of a total of 937 people surveyed, 113 have both asthma and at least one family member who smokes. What is the probability that a randomly selected survey participant has both a family member who smokes and asthma. (round to the nearest tenth)
12% of the participants have a family member who smokes and asthma.
If you were to shade a Venn diagram to represent that neither of the two events represented in the diagram are occurring, would you shade the center section, right section, left section, both sections, or outside of the diagram?
You would shade outside of the diagram.
How do you denote the conditional probability of event A occurring, given that event B has occurred?
This is denoted as P(A|B)
Define what a compound probability is.
A compound probability is the likeliness of two independent events occurring.
805 total people were surveyed. 175 of them were currently studying engineering and 630 of them were not. What is the probability that a randomly selected survey participant is studying engineering? (round to the nearest tenth)
21.7% are studying engineering
Of 937 people surveyed, 473 neither have asthma nor a family member who smokes. What is the probability that a randomly selected survey participant has neither asthma nor a family member who smokes. (round to the nearest tenth)
There is a 50% chance that a randomly selected survey participant has neither asthma nor a family member who smokes.
If you were to shade a Venn diagram to represent only one of the two shown events, would you shade the right or left sections, the center section, or the left and right sections?
You would shade the right or left sections.
A survey of 70 high school students revealed that 35 like folk music, 15 like classical music, and 5 like both. Draw Venn diagram and decide how many of the students surveyed do not like either folk or classical music?
25 students
What is the formula of addition rule (mutually exclusive event)?
P (A Or B) = P(A) + P(B) - P (A and B)
182 of the surveyed students have asthma. Of these students, 69 of them have a household member who smokes, and 113 of them do not What is the probability that a student has a household member who smokes? (round to the nearest tenth)
37.9% have a household member who smokes
Of a total of 515 surveyed people, 91 are both male and rated the library as good. What is the probability that that a randomly selected survey participant is both Male and rates the library as good? (round to the nearest tenth)
The probability that a randomly selects person is both male and rates the library as good is 18%
Of the 400 people on a flight, 368 have checked baggage, 228 have checked baggage but do not have frequent flier status, and 8 have neither frequent flier status nor checked baggage. Use a Venn diagram to to solve for the probabilities of each event occurring.
6% have frequent flier status only, 57% have checked baggage only, 35% have both checked baggage and frequent flier status, and 2% have neither frequent flier status nor checked baggage.
The probability of one or the other event occurring can be described by what term?
The probability that one or the other event occur is the union between one event and another.
What is the rule of subtraction in probabilities?
P(not A) = 1 - P(A)
114 total people were surveyed. Of these 114 people, 6 were between the ages 18-25, 44 were between the ages 26-40, 35 were between the ages 41-65, and 24 were 66 and older. What is the probability that a randomly selected survey participant will be between the ages 18-25? (round to the nearest tenth)
5.3% were between the ages 18-25
Of 805 total people surveyed, 40 are both in the marching band and in an engineering major. What is the probability that a randomly selected person is both in the marching band and in an engineering major? (round to the nearest tenth)
The probability that a randomly selected person is both in the marching band and in an engineering major is 4%
The probability that a randomly selected animal is North American is 0.65, the probability that it is both North American and a carnivore is 0.16, and the probability that it is neither a carnivore nor a carnivore is 0.17. Use a Venn diagram to determine the probability that an animal is a carnivore.
The probability that an animal is a carnivore is 18%
What word describes two events when one event's occurrence changes the probability of another event?
In this situation, the two events are described as dependent.
What is the rule of multiplication in probabilities?
P(A∩B) = P(B)×P(A|B) = P(A)×P(B|A)