4. A coin is flipped and a die is rolled. Find the probability of getting a head on the coin and a 4 on

the die.

5. A card is drawn from a deck and replaced, then a second card is drawn. Find the probability of

getting a queen and then an ace.

6. A Harris poll found that 46% of Americans say they suffer great stress at least once a week. If three

people are selected at random, find the probability that all three wills say that they suffer great stress

at least once a week.

7. If the probability of giving birth to a boy is 0.52, what is the probability of giving birth to four

consecutive boys?

8. At a local university 54.3% of incoming first-year students have computers. If 3 students are

selected at random, find the following probabilities.

a) None have computers

b) All have computers.

Playing Card Cheat Sheet:

5.3 Binomial Probability

There are many probability experiments for which the results of each trial can be reduced to

outcomes:

ex: when a basketball player attempts a free throw. What can happen?

A has these important features:

There are a number of trials

Each trial has possible outcomes

The trials are

the outcome of one trial the probability of success on any

other trial.

The probability of each outcome is throughout the trials

There are two outcomes for a binomial experiment:

Notation

Symbol Description

Are you right or left handed?

1. In a tennis league, 80% of the players are right-handed. The league president is randomly selecting

seven players to demonstrate serves. What is the probability that exactly three of the selected

players will be right-handed?

Just one more card…

2. Hockey cards, chosen at random from a set of 20, are given away inside cereal boxes. Stan needs

one more card to complete his set so he buys five boxes of cereal. What is the probability that he will

complete his set?

Let’s play ball!

3. While pitching for the Toronto Blue Jays, 4 of every 7 pitches Juan Guzman threw in the first 5

innings were strikes. What is the probability that 3 of the next 4 pitches will be strikes?

I don’t know this stuff!

4. A true-false test has 12 questions. Suppose you guess all 12. What is the probability of exactly

seven correct answers?

I won!!!!

5. As part of a promotion, a store is giving away scratch-off cards. Each card has a 40% chance of

awarding a prize. Suppose you have 5 cards. Find the probability that exactly four of the five cards

will reveal a prize.

I’ve been hacked.

6a. Privacy is a concern for many users of the Internet. One survey showed that 59% of Internet users

are somewhat concerned about the confidentiality of their e-mail. Based on this information, what is

the probability that for a random sample of 10 Internet users, 6 are concerned about the privacy of

their e-mail?

At least

In many cases, we will be interested in the probability of a rather than in

the probability of an exact number of successes.

ex: What is the probability that 6 of the 10 Internet users have concerns about

privacy.

I’ve been hacked again.

6b. Privacy is a concern for many users of the Internet. One survey showed that 59% of Internet users

are somewhat concerned about the confidentiality of their e-mail. Based on this information, what is

the probability that for a random sample of 10 Internet users, at least 6 are concerned about the

privacy of their e-mail?

Ketchup

7. A biologist is studying a new hybrid tomato. It is known that the seeds of this hybrid tomato have

probability 0.70 of germinating. The biologist plants 10 seeds.

a) What is the probability that exactly 8 seeds will germinate?

b) What is the probability that at least 8 seeds will germinate?

8. Sociologists say that 90%of married women claim that their husband’s mother is a horrible person.

Suppose that six married women are having coffee together one morning. What is the probability

that:

a) All of them dislike their mother-in-law?

b) none of them dislike their mother-in-law?

c) at least four of them dislike their mother- in-law?

d) no more than three of them dislike their mother in-law?

9. It is reported that 77% of workers aged 16 and over drive to work alone. Choose 8 workers at

random. Find the probability that

a) all drive to work alone

b) 4 or more drive to work alone

c) Exactly 3 drive to work alone

5.4 Normal Distribution

The term bell curve is used to describe the mathematical concept called normal

distribution. The center contains the greatest number of a value and therefore

would be the highest point on the arc of the line. This point is referred to the

_____________ but in simple terms it is the highest number of occurrences

of an element.

The important things to note about a normal distribution is the curve is ______________________in

the center and decreases on either side.

This is significant in that the data has less of a tendency to produce unusually extreme values,

called outliers, as compared to other distributions.

A bell curve graph depends on two factors, __________________________________________.

There are two symbols each that can represent the mean and the standard deviation.

mean –

standard deviation –

When we have a normal distribution with mean µ and standard deviation σ,

we use the notation: _____________

1. Write the notation for a normal distribution with a mean of 0 and standard deviation of 1.

68-95-99.7 Rule

In terms of probability, once we determine that the data is normally distributed (bell curved)

and we calculate the mean and standard deviation, we are able to determine the probability

that a single data point will fall within a given range of possibilities.

___________of the data values fall within _____ standard

deviation of the mean in either direction

___________of the data values fall within _____ standard

deviation of the mean in either direction

___________of the data values fall within _____ standard

deviation of the mean in either direction