# Marginal & Conditional Probabilities

Section 3.1: Basic Concepts of Probability and Counting

1. License plates are made using 2 letters followed by 3 digits. How many different plates can be made if repetition of letters and digits is allowed? (References: example 4 page 135, end of section exercises 13 - 16 page 142 and 35 - 36 page 144)

2. In 2005 the stock market took some big swings up and down. One thousand investors were asked how often they tracked their investments. The table below shows their responses. What is the probability that an investor tracks the portfolio monthly? (References: example 6 page 137, end of section exercises 45 - 48 page 145)

How often tracked? Response

Daily 235

Weekly 278

Monthly 292

Few times a year 136

Do not track 59

Section 3.2: Conditional Probability and the Multiplication Rule

3a. In a battleground state, 40% of all voters are Republicans. Assuming that there are only two parties - Democrat and Republican, if two voters are randomly selected for a telephone survey, what is the probability that they are both Republicans? Round your answer to 4 decimal places (References: example 4 page 152, end of section exercises 19 - 21 page 156 - 157)

b. You are dealt 2 cards from a shuffled deck of 52 cards, without replacement. There are four suits of 13 cards each in a deck of cards; two of them are black and two of them are red. What is the probability that both cards are black? Round your answer to 3 decimal places (References: example 3 page 151.

4. The table below shows the drink preferences for people in 3 different age groups. If one of the 255 subjects is randomly chosen, what is the probability that the person drinks cola given they are over 40? Round your answer to 3 decimal places. (References: example 4 and 5 page 152 - 153, end of section exercises 15, 16, 23 , 24 page 156)

Water Orange juice Cola

Under 21 years 40 25 20

21 - 40 years 35 20 30

Over 40 years 20 30 35

Section 3.3: The Addition Rule

5. a. The table below shows the drinking habits of adult men and women.

Non-Drinker Occasional Drinker Regular Drinker Heavy Drinker Total

Men 387 45 90 37 559

Women 421 46 69 34 570

Total 808 91 159 71 1,129

If one of the 1,129 people is randomly chosen, what is the probability that the person is a man or a non-drinker? Round your answer to 3 decimal places. (References: example 4 page 163, end of section exercises 23 - 26 page 168 - 169)

b. The table show drinking habits of adult men and women.

Non-Drinker Occasional Drinker Regular Drinker Heavy Drinker Total

Men 387 45 90 37 559

Women 421 46 69 34 570

Total 808 91 159 71 1,129

If one of the 1,129 people is randomly chosen, what is the probability that the person is a non-drinker or a heavy drinker? Round your answer to 3 decimal places. (References: example 4 page 163, end of section exercises 23 - 26 page 168 - 169)

#### Solution Summary

The solution provides step by step method for the calculation of probabilities and conditional probabilities. Formula for the calculation and Interpretations of the results are also included.