Probability and counting rules

Sample Spaces and Probability

Mathematical Statistics with Applications 7th

According to the Washington Post, nearly 45\% of all Americans are born with brown eyes, although their eyes don't necessarily stay brown. $^{\star}$ A random sample of 80 adults found 32 with brown eyes. Is there sufficient evidence at the .01 level to indicate that the proportion of brown eyed adults differs from the proportion of Americans who are born with brown eyes?

Hypothesis Testing

Common Large-Sample Tests

03:03

Mathematical Statistics with Applications 7th

The hourly wages in a particular industry are normally distributed with mean $\$ 13.20$ and standard deviation $\$ 2.50 .$ A company in this industry employs 40 workers, paying them an average of $\$ 12.20$ per hour. Can this company be accused of paying substandard wages? Use an $\alpha=.01$ level test.

Hypothesis Testing

Common Large-Sample Tests

01:00

Elementary Statistics a Step by Step Approach

Population of Hawaii The population of Hawaii is $22.7 \%$ white, $1.5 \%$ African-American, $37.7 \%$ Asian, $0.2 \%$ Native American/Alaskan, $9.46 \%$ Native Hawaiian/Pacific Islander, $8.9 \%$ Hispanic, $19.4 \%$ two or more races, and $0.14 \%$ some other. Choose one Hawaiian resident at random. What is the probability that he/she is a Native Hawaiian or Pacific Islander? Asian? White?

Probability and Counting Rules

Sample Spaces and Probability

The Addition Rules for Probability

6 Practice Problems

04:50

Elementary Statistics 13th

Probability of a Run of Four Use a simulation approach to find the probability that when six consecutive babies are born, there is a run of at least four babies of the same sex. Describe the simulation procedure used, and determine whether such runs are unlikely.

Probability

Probabilities Through Simulations

04:35

Elementary Statistics 13th

Describe the simulation procedure. (For example, to simulate 10 births, use a random number generator to generate 10 integers between 0 and 1 inclusive, and consider 0 to be a male and 1 to be a female.)
Lefties Ten percent of people are left-handed. In a study of dexterity, 15 people are randomly selected. Describe a procedure for using software or a TI- $83 / 84$ Plus calculator to simulate the random selection of 15 people. Each of the 15 outcomes should be an indication of one of two results: (1) Subject is left-handed; (2) subject is not left-handed.

Probability

Probabilities Through Simulations

02:56

Elementary Statistics 13th

Simulating Coin Flips One student conducted the simulation described in Example 3 and stated that the probability of getting a sequence of six 0s or six 1s is 0.977. What is wrong with that statement?

Probability

Probabilities Through Simulations

The Multiplication Rules and Conditional Probability

8 Practice Problems

01:48

Elementary Statistics 11th

Identical and Fraternal Twins. Use the data in the following table. Instead of summarizing observed results, the entries reflect the actual probabilities based on births of twins (based on data from the Nortbern California Tivin Registry and the article "Bayesians, Frequentists, and Scientists" by Bradley Efron, Journal of the American Statistical Association, Vol. $100,$ No. 469 ). Identical twins come from a single egg that splits into two embryos, and fraternal twins are from separate fertilized eggs. The table entries reflect the principle that among sets of twins, I/3 are identical and $2 / 3$ are fraternal. Also, identical twins must be of the same sex and the sexes are equally likely (approximately), and sexes of fraternal twins are equally likely. $$\begin{array}{lcccc} & \multicolumn{3}{c} {\text { Sexes of Twins }} \\& \text { boy/boy } & \text { boy/girl } & \text { girl/boy } & \text { girl/gin } \\\hline \text { Identical Twins } & 5 & 0 & 0 & 5 \\\text { Fraternal Twins } & 5 & 5 & 5 & 5\end{array}$$
Fraternal Twins If a pregnant woman is told that she will give birth to fraternal twins, what is the probability that she will have one child of each sex?

Probability

Multiplication Rule: Complements and Conditional Probability

01:01

College Algebra

Use the Multiplication Property of Probabilities.
If $P(A)=0.3$ and $P(B | A)=0.6,$ find $P(A \cap B)$

Sequences, Series, and Probability

Probability

01:38

College Algebra

Assume that the probability that an airplane engine will fail during a torture test is $\frac{1}{2}$ and that the aircraft in question has 4 engines.
Find the probability that exactly 2 engines will survive.

Sequences, Series, and Probability

Probability

Counting Rules

12 Practice Problems

00:19

Algebra and Trigonometry 10e

A woman has 5 blouses and 8 skirts. How enany different outfits can she wear?

Counting and Probability

Counting

00:26

Algebra and Trigonometry 10e

Use the information given in the figure.
How many are in set $A ?$

Counting and Probability

Counting

01:01

Algebra and Trigonometry 10e

The Counting Formula states that if $A$ and $B$ are finite sets, then $n(A \cup B)=$ ___>

Counting and Probability

Counting

23 Practice Problems

00:23

Prealgebra

Simplify.
$$\frac{6 \cdot 5}{2 \cdot 1}$$

More Statistics and Probability

Counting Outcomes

00:51

Prealgebra

The spinner is spun twice. What is the probability that it will land on
2 after the first spin and on 5 after the second spin?
F $\frac{1}{64}$
G $\frac{1}{16}$
H $\frac{1}{8}$
J $\frac{5}{8}$

More Statistics and Probability

Counting Outcomes

00:44

Prealgebra

The table shows the features you can choose to customize a computer.
CAN'T COPY THE TABLE
How many customized computers include the 17-inch flat panel monitor?

More Statistics and Probability

Counting Outcomes