0.15 More probability: homework

A coin is tossed ten times. Find the probability of getting six heads and four tails.

A family has three children. Find the probability of having one boy and two girls.

What is the probability of getting three aces(ones) if a die is rolled five times?

A baseball player has a .250 batting average. What is the probability that he will have three hits in five times at bat?

A basketball player has an 80% chance of sinking a basket on a free throw. What is the probability that he will sink at least three baskets in five free throws?

With a new flu vaccination, 85% of the people in the high risk group can go through the entire winter without contracting the flu. In a group of six people who were vaccinated with this drug, what is the probability that at least four will not get the flu?

A transistor manufacturer has known that 5% of the transistors produced are defective. What is the probability that a batch of twenty five will have two defective?

It has been determined that only 80% of the people wear seat belts. If a police officer stops a car with four people, what is the probability that at least one person will not be wearing a seat belt?

What is the probability that a family of five children will have at least three boys?

What is the probability that a toss of four coins will yield at most two heads?

A telemarketing executive has determined that for a particular product, 20% of the people contacted will purchase the product. If 10 people are contacted, what is the probability that at most 2 will buy the product?

To the problem: "Five cards are dealt from a deck of cards, find the probability that three of them are kings," the following incorrect answer was offered by a student.

What change would you make in the wording of the problem for the given answer to be correct?

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.

1. $P\left(\text{marble is red}\right)$

2. $P\left(\text{It came from Jar II given that the marble drawn is white}\right)$

3. $P\left(\text{Red}\mid \text{Jar I}\right)$

In Mr. Symons' class, if a person does his homework most days, his chance of passing the course is 90%. On the other hand, if a person does not do his homework most days his chance of passing the course is only 20%. Mr. Symons claims that 80% of his students do their homework on a regular basis. If a student is chosen at random from Mr. Symons' class, find the following probabilities.

1. $P\left(\text{the student passes the course}\right)$

2. $P\left(\text{the student did homework}\mid \text{the student passes the course}\right)$

3. $P\left(\text{the student passes the course}\mid \text{the student did homework}\right)$