# Computing probability using the Rule of Addition

In our virtual world, we own a construction company and bid on projects. Based on our past history of winning bids on projects, the probability of winning the next contract to build a school is 0.40, to build a hospital is 0.30 and to build both a school and a hospital is 0.20. What is the probability of winning a contract to build either the school or the hospital? The school only? The hospital only?

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#### Solution Preview

We need use the Rule of Addition.

So P(build either the school or the hospital)=P(build the ...

#### Solution Summary

The solution gives detailed steps on computing the probability using the Rule of Addition.

Statistics - General Questions

General Questions on Probability and Analysis of Variance.

STATISTICS QUESTIONS:

1. Which of the following is a correct statement about a probability?

a. Probability values range from 0 to 1, inclusive.

b. Probabilities may assume negative values.

c. Probabilities may be greater than 1.

d. Probabilities are limited to one decimal place.

2. The definition of a probability is

a. a number between 0 and 1, inclusive.

b. the outcome of an experiment.

c. the likelihood that an event will happen.

d. an uncertain event.

3. An event is

a. collection of events.

b. A collection of outcomes from an experiment.

c. Always greater than 1.

d. The act of taking a measurement or the observation of some activity.

4. Which of the following is not a type of probability?

a. Subjective

b. Independent

c. Empirical

d. Classical

5. Two events are independent if

a. event prevents the occurrence of the other event.

b. The sum of their probabilities is greater than 1.

c. We can count the possible outcomes.

d. The probability of one event happening does not affect the probability of another event happening.

6. Two events are not independent if

a. One event prevents the occurrence of the other event.

b. The sum of their probabilities is greater than 1.

c. We can count the possible outcomes.

d. The probability of one event happening does not affect the probability of another event happening.

7. The Special Rule of Addition is used to compute

a. The probability of two or more Independent events.

b. The probability of two or more mutually exclusive events

c. The probability of collectively exhaustive events.

d. Subjective probabilities

8. The joint probability of two mutually exclusive events is

a. Zero.

b. One.

c. 0.50.

d. The sum of the probabilities of both events.

9. The General Rule of Multiplication is used to compute

a. The probability of two or more dependent events.

b. The probability of two or more independent events.

c. The probability of two or more mutually exclusive events.

d. Subjective probabilities

10. When we find the probability of an event by subtracting the probability of the event not happening from 1, we are using

a. Subjective probability

b. The complement rule.

c. The general rule of addition.

d. The special rule of multiplication

1. An F-statistic is used to

a. Test if the MSE equals 0

b. Test the equality of two population variances.

c. Test if a z-statistic is greater than 0.

d. Convert a z statistic to a t statistic.

2. An F-distribution is

a. Positively skewed.

b. Symmetric.

c. Negatively skewed.

d. Uniform.

3. ANOVA is a statistical technique used to test a null hypothesis of equal population

a. variances.

b. proportions.

c. means.

d. skewness.

4. The result of an ANOVA hypothesis test is based on the ratio of

a. treatment and error mean squares.

b. total and error mean squares.

c. total and treatment squares.

d. two treatment variances

5. Which of the following is a characteristic of the F distribution?

a. It is a discrete distribution.

b. It cannot be positive.

c. It is based on the ratio of variances from two populations.

d. It is the ratio of two population means.

6. The term "Treatment" refers to

a. source of variation.

b. The numerator degrees of freedom.

c. The variation within the cells.

d. Error variation.

7. ANOVA requires that the

a. populations are normally distributed.

b. populations have equal means.

c. samples are dependent.

d. population variances are not equal.

8. Under which of the following conditions will the computed value of F be negative?

a. When there is no difference in the treatment means

b. When there is no difference in the block means

c. When the SS total is larger than SST.

d. F cannot be negative.

9. Suppose we conduct an ANOVA test of four treatment means. Construction of a confidence interval for the difference between the first and second sample means is ( ). From this information we know:

a. This pair of means is statistically different.

b. This pair of means is not statistically different.

c. The null hypothesis was accepted ( or not rejected).

d. The error degrees of freedom equal 27.

10. If H0: ? 1 = ? 2 = ? 3 = ? 4 is rejected, we conclude that

a. All treatment means are not equal.

b. Three of the treatment means are not equal.

c. At least one pair of treatment means are not equal.

d. All treatment variances are not equal.