Do the following problems using the binomial probability formula.

### Exercise 1

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

#### Solution

0.2051

### Exercise 2

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

### Exercise 3

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

#### Solution

0.0322

### Exercise 4

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

### Exercise 5

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?

#### Solution

0.9421

### Exercise 6

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?

### Exercise 7

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?

#### Solution

0.2305

### Exercise 8

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?

### Exercise 9

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

#### Solution

0.5

### Exercise 10

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

### Exercise 11

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?

#### Solution

0.6778

### Exercise 12

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?

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