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Jar I contains five red and three white marbles, and Jar II contains four red and two white marbles. A jar is picked at random and a marble is drawn. Draw a tree diagram below, and find the following probabilities.
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P(marble is red)
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P(It came from Jar II | marble is white)
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P(Red | Jar I)
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In Mr. Symons' class, if a student does homework most days, the chance of passing the course is 90%. On the other hand, if a student does not do homework most days, the chance of passing the course is only 20%.
H = event that the student did homework
C = event that the student passed the course
Mr. Symons claims that 80% of his students do homework on a regular basis. If a student is chosen at random from Mr. Symons' class, find the following probabilities.
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P(C)
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P(H|C)
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P(C|H)
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A city has 60% Democrats, and 40% Republicans. In the last mayoral election, 60% of the Democrats voted for their Democratic candidate while 95% of the Republicans voted for their candidate. Which party's mayor runs city hall?
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In a certain population of 48% men and 52% women, 56% of the men and 8% of the women are color-blind.
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What percent of the people are color-blind?
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If a person is found to be color-blind, what is the probability that the person is a male?
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A test for a certain disease gives a positive result 95% of the time if the person actually carries the disease. However, the test also gives a positive result 3% of the time when the individual is not carrying the disease. It is known that 10% of the population carries the disease. If a person tests positive, what is the probability that he or she has the disease?
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A person has two coins: a fair coin and a two-headed coin. A coin is selected at random, and tossed. If the coin shows a head, what is the probability that the coin is fair?
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A computer company buys its chips from three different manufacturers. Manufacturer I provides 60% of the chips and is known to produce 5% defective; Manufacturer II supplies 30% of the chips and makes 4% defective; while the rest are supplied by Manufacturer III with 3% defective chips. If a chip is chosen at random, find the following probabilities:
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P(the chip is defective)
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P(chip is from Manufacturer II | defective)
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P(defective |chip is from manufacturer III)
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Lincoln Union High School District is made up of three high schools: Monterey, Fremont, and Kennedy, with an enrollment of 500, 300, and 200, respectively. On a given day, the percentage of students absent at Monterey High School is 6%, at Fremont 4%, and at Kennedy 5%. If a student is chosen at random, find the probabilities below:
Hint: Convert the enrollments into percentages.
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P(the student is absent)
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P(student is from Kennedy | student is absent)
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P(student is absent | student is from Fremont)
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9. At a retail store, 20% of customers use the store’s online app to assist them when shopping in the store ; 80% of store shoppers don’t use the app.
Of those customers that use the online app while in the store, 50% are very satisfied with their purchases, 40% are moderately satisfied, and 10% are dissatisfied.
Of those customers that do not use the online app while in the store, 30% are very satisfied with their purchases, 50% are moderately satisfied and 20% are dissatisfied.
Indicate the events by the following:
A = shopper uses the app in the store
N = shopper does not use the app in the store
V = very satisfied with purchase
M = moderately satisfied
D = dissatisfied
a. Find P(A and D), the probability that a store customer uses the app and is dissatisfied
b. Find P(A|D), the probability that a store customer uses the app if the customer is dissatisfied.
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10. A medical clinic uses a pregnancy test to confirm pregnancy in patients who suspect they are pregnant. Historically data has shown that overall, 70% of the women at this clinic who are given the pregnancy test are pregnant, but 30% are not.
The test's manufacturer indicates that if a woman is pregnant, the test will be positive 92% of the time.
But if a woman is not pregnant, the test will be positive only 2% of the time and will be negative 98% of the time.
a. Find the probability that a woman at this clinic is pregnant and tests positive.
b. Find the probability that a woman at this clinic is actually pregnant given that she tests positive.
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