Solve the problem:
Basic Concepts of Probability and Counting
Q1. 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?
Q2. 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?
How often tracked? Response
Daily 235
Weekly 278
Monthly 292
Few times a year 136
Do not track 59
Conditional Probability and the Multiplication Rule
Q3a. 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
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?
Q4. 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?
Water Orange juice Cola
Under 21 years 40 25 20
21 - 40 years 35 20 30
Over 40 years 20 30 35
The Addition Rule
Q5. 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.
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.