Solved Problems in Probability and Statistics
Probability and Statistics Problems: Solutions
1. FSU Volleyball Team: Probability of Losing Both Games
The probability that the FSU volleyball team wins a game is 0.8. If the team has two games this weekend, assuming independence of events, what is the probability that the team will lose both games?
P(A) = (1 – 0.8) = 0.2
P(B) = (1 – 0.8) = 0.2
P(losing both games) = 0.2 x 0.2 = 0.04
2. Probability of at Least Two Female Babies
If a girl gives birth to 3 babies, what is the probability that she would give birth to at least two females?
The probability is 0.5
3. Combination Lock: Possible Opening Numbers
A combination lock system has four ten-digit (0 to 9) number wheels side by side. How many four-digit opening numbers are possible if a digit cannot be used more than once and the first digit cannot be number zero?
9 x 9 x 8 x 7 = 4536
4. Selecting a Group: Combinations
FSU wants to select 3 men and 2 women from a group of 10 men and 6 women that are available. How many ways can the group of five (5) persons be selected?
This problem requires calculating combinations, but the solution is not provided in the original text.
5 & 6. Refrigerator Production: Distribution Analysis
A refrigerator manufacturer has an average daily production of 125 units, with a standard deviation of 15 units per day. If the refrigerator production distribution is mound-shaped:
5. Percentage of Days with Production Between 110 and 155 Units
The solution is not provided in the original text.
6. Percentage of Days with Production Over 140 Units
X > 140 = 16%
7, 8, & 9. Roulette Probabilities
In roulette, there are 38 slots in which a ball may land. There are numbers: 0, 00, and 1-36. The odd numbers are red and even are black, and zeros are green. A ball is thrown:
7. Probability of Getting a Multiple of Five
5, 10, 15, 20, 25, 30, 35 (7 numbers)
7/38 = 0.18
8. Probability of a Number Higher than 20 and a Multiple of Three
21, 24, 27, 30, 33, 36 (6 numbers)
6/38 = 0.15
9. Probability of a Number Higher than 32
33, 34, 35, 36 (4 numbers)
4/38 = 0.1052
10. Deli Sandwiches: Possible Combinations
A deli serves meat sandwiches with the following options: three kinds of bread, five kinds of meat, and the option of four different types of cheese. How many different types of sandwiches are possible, assuming one item is used out of each group?
3 x 5 x 4 = 60
11, 12, 13, & 14. Adult Population Probabilities
The accompanying table describes the adult population of a small suburb of a large city. (Table data is missing from the original text). What is the probability that:
11. Income Over $50,000
2550/8000 = 0.318
12. Income of $20,000 – $50,000 Given Age Under 25
P(A/B) = P(A and B) / P(B)
1000/8000 / 2000/8000 = 1000/2000 = 0.5
13. Over 45 or Income Under $20,000
P(A or B) = P(A) + P(B) – P(A and B)
= 2000/8000 + 1450/8000 – 50/8000 = 3400/8000 = 34/80 = 0.425
14. 25 or More Years and Income of $20,000 or More
2050 + 1500 = 3550
950 + 1000 = 1950
3550 + 1950 = 5500
5500/8000 = 0.6875
15. Cell Phone Sales: Weighted Mean Profit
The sales statistics of local cell phones are as follows:
- Company A: $7,000,000 sales, 6% profit
- Company B: $12,000,000 sales, 7% profit
- Company C: $5,000,000 sales, 8% profit
What is the weighted mean profit for the sale of local cell phones?
xw = Σxiwi / Σwi
= 166,000,000 / 24,000,000 = 6.92%
16. Shoe Color Selection: Probability
A manufacturing firm has 9 shoe colors available (red, blue, etc.), and has to select 3 shoe colors. What is the probability that the red shoe color is selected?
3/9 x 8/8 x 7/7 = 168/504 = 1/3
17. Business Venture: Probability of Failure
A business venture can result in the following outcomes with their corresponding chance of occurrence shown in parenthesis: highly successful (15%), successful (25%), break-even (30%), and failure (?). If these are the only outcomes possible for the business venture, what is the chance or probability that the business venture will be a failure?
100% – (15% + 25% + 30%) = 30%
18, 19, & 20. Sales Commissions Analysis
Given the following tables: (Table data is missing from the original text).
18. Arithmetic Mean of Commissions
x̄ = Σxi / n = 4455 / 21 = 212.14
19. Median Commission
Median = ½ (21) = 10.5 ~ 11th value
Median is 205
20. Standard Deviation of Commissions
The solution is not provided in the original text.