## Exercises for Finite Mathematics Applied to the Real World This Topic: Probability

Enter your answer for each question in the left box, and press "Check." If you use decimals, they must be accurate to 4 decimal places. You can also use fraction notation, eg. 33/56.

1. In Advanced Carmine Canasta, in each player rools two dice (one red, one green), flips a coin, and selects three gummy bears from a package containing two rasberry ones, two lime ones and two orange ones.

 (a) How many outcomes are possible? (b) To have a winning conbination, both dice must show the same number, the coin toss must result in heads, and two of the gummy bears must be lime. What is the probability of winning Advanced Carmine Canasta?

2. The following table shows sales of luxury imported vehicles in the US in 1996-1998.

 Acura Infiniti Lexus Mercedes Total 1996 60,000 55,000 80,000 90,000 285,000 1997 70,000 65,000 95,000 120,000 350,000 1998 65,000 55,000 140,000 155,000 415,000 Total 195,000 175,000 315,000 365,000 1,050,000

Figures are rounded, and 1998 figures are annualized, based on sales through September. Source: Ward's Automobiles/The New York Times, October 21, 1998, p. C1.

Calculate the following (experimental) probabilities:

 (a) That a luxury imported vehicle purchased during 1996-1998 was an Acura (b) That a luxury imported vehicle purchased during during 1996-1998 was an Acura, given that it was an import from Japan (c) That a luxury vehicle was purchased after 1996, given that it was an import from Japan

3. A consumer survey reveals that the probability of a computer owner shopping on the Internet was 0.17, while the probability of a computer owner downloading software was 0.33. Further, the probability a computer owner doing both was 0.14. Find the probability of the following events:

 (a) that a computer owner does not shop on the Internet (b) that a computer owner will either shop on the Internet or download software (c) that a computer owner will neither shop on the Internet nor download software

4. The moon is in the Seventh House at the same time that Jupiter aligns with Mars 5% of the time, whereas Jupiter aligns with Mars 25% of the time. It is also found that, 75% of the time, either Jupiter aligns with Mars or the Moon is in the Seventh House, or both. What percentage of the time is the Moon in the Seventh House?

% of the time

5. Based on past statistics, 60% of finite math students who use this web site get high grades, whereas 15% of all finite math students use this web site and get a high grade. What is the probability that a finite math student uses this web site?

6. Two dice (one red, one green) are cast, and the uppermost numbers are observed. Test for independence (make a choice and press "Check"):

 (a) The red die is even; the green die is odd dependent independent (b) The red die is a 1; the sum is even dependent independent (c) Neither die is 1; the sum is even dependent independent (d) Both dice are 1; the sum is even dependent independent (e) Neither die is 1; both show the same number dependent independent

7. The moon is in the Seventh House once every 30 days on average, and when it is, Jupiter has a 10% chance of aligning with Mars; when it isn't, Jupiter has only a 5% chance of aligning with Mars.

 (a) What is the probability that the moon is in the Seventh House when Jupiter aligns with Mars? (b) What is the probability that the moon is in the Seventh House and Jupiter aligns with Mars?

Last Updated:March, 1999