0.15 More probability: homework  (Page 2/5)

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?

In a certain population of 48% men and 52% women, 56% of the men and 8% of the women are color-blind.

1. What percent of the people are color-blind?

2. If a person is found to be color-blind, what is the probability that the person is a male?

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 the test is positive for a person, what is the probability that he or she has the disease?

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?

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.

1. $P\left(\text{the chip is defective}\right)$

2. $P\left(\text{it came from Manufacturer II}\mid \text{the chip is defective}\right)$

3. $P\left(\text{the chip is defective}\mid \text{it came from manufacturer III}\right)$

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 following probabilities. Hint: Convert the enrollments into percentages.

1. $P\left(\text{the student is absent}\right)$

2. $P\left(\text{the student came from Kennedy}\mid \text{the student is absent}\right)$

3. $P\left(\text{the student is absent}\mid \text{the student came from Fremont}\right)$

You are about to make an investment which gives you a 30% chance of making $60,000 and 70% chance of losing $ 30,000. Should you invest? Explain.

In a town, 40% of the men and 30% of the women are overweight. If the town has 46% men and 54% women, what percent of the people are overweight?

A game involves rolling a Korean die (4 faces). If a one, two, or three shows, the player receives the face value of the die in dollars, but if a four shows, the player is obligated to pay $4. What is the expected value of the game?

A game involves rolling a single die. One receives the face value of the die in dollars. How much should one be willing to pay to roll the die to make the game fair?

In a European country, 20% of the families have three children, 40% have two children, 30% have one child, and 10% have no children. On average, how many children are there to a family?