How can you use the general addition rule to find the probability of occurrence of event A or B?

A daily lottery is conducted in which 2 winning numbers are selected out of 100 numbers. How many different combinations of winning numbers are possible?

For each of the following, indicate whether the type of probability involved is an example of a priori probability, empirical probability, or subjective probability.

a. The next toss of a fair coin will land on heads.

b. Italy will win soccer's World Cup the next time the competition is held.

c. The sum of the faces of two dice will be seven.

d. The train taking a commuter to work will be more than 10 minutes late.

A student has seven books that she would like to place in her backpack. However, there is room for only four books. Regardless of the arrangement, how many ways are there of placing four books into the backpack?

Four members of a group of 10 people are to be selected to a team. How many ways are there to select these four members?

How many different ways can a senior project manager and an associate project manager be selected for an analytics project if there are eight data scientists available?

A gardener has six rows available in his vegetable garden to place tomatoes, eggplant, peppers, cucumbers, beans, and lettuce. Each vegetable will be allowed one and only one row. How many ways are there to position these vegetables in this garden?

In the National Basketball League there are five teams in the Pacific Division: Golden State, Los Angeles Clippers, Los Angeles Lakers, Phoenix, and Sacramento. How many different orders of finish are there for these five teams? (Assume that there are no ties in the standings.) Do you believe that all these orders are equally likely? Discuss.

Referring to the above Problem how many different orders of finish are possible for the first four positions?

In the National Basketball League there are five teams in the Pacific Division: Golden State, Los Angeles Clippers, Los Angeles Lakers, Phoenix, and Sacramento. How many different orders of finish are there for these five teams? (Assume that there are no ties in the standings.) Do you believe that all these orders are equally likely? Discuss.

A team is being formed that includes four different people. There are four different positions on the teams. How many different ways are there to assign the four people to the four positions?

You would like to ”build-your-own-burger” at a fast-food restaurant. There are five different breads, seven different cheeses, four different cold toppings, and five different sauces on the menu. If you want to include one choice from each of these ingredient categories, how many different burgers can you build?

A particular brand of women's jeans is available in seven different sizes, three different colors, and three different styles. How many different women's jeans does the store manager need to order to have one pair of each type?

a. If a coin is tossed seven times, how many different outcomes are possible?

b. If a die is tossed seven times, how many different outcomes are possible?

c. Discuss the differences in your answers to (a) and (b).

Consider the following contingency table:

$$\begin{array}{ccc} & \boldsymbol{B} & \boldsymbol{B}^{\prime} \\ \hline \boldsymbol{A} & 10 & 30 \\ \boldsymbol{A}^{\prime} & 25 & 35 \end{array}$$

What is the probability of event

a. $A^{\prime}$ ?

b. A and B ?

c. $A^{\prime}$ and $B^{\prime}$ ?

d. $A^{\prime}$ or $B^{\prime}$ ?