Discrete Probability Distributions 2425 shema final.ppt
- 2. Find the probability of the following events: 1. Getting an even number in a single roll of dice. 2. Getting a sum of 6 when two dice are rolled. 3. Getting an ace when a card is drawn from a deck. 4. The probability that all the children are boys if a couple has three children. 5. Getting an odd number and a tail when a die is rolled and a coin is tossed simultaneously. 5-Minute Drill
- 3. Find the probability of the following events: 6. Getting a sum of 11 when two dice are rolled. 7. Getting a black card and a 10 when a card is drawn from a deck. 8. Getting a red queen when a card is drawn from a deck. 9. Getting doubles when two dice are rolled. 10. Getting a red ball from a box containing 3 red and 6 black balls. 5-Minute Drill
- 4. Key:
- 5. Key:
- 6. Key:
- 7. Key:
- 8. Find the probability of the following events: 6. Getting a sum of 11 when two dice are rolled. 7. Getting a black card and a 10 when a card is drawn from a deck. 8. Getting a red queen when a card is drawn from a deck. 9. Getting doubles when two dice are rolled. 10. Getting a red ball from a box containing 3 red and 6 black balls. 5-Minute Drill
- 9. Decision making is an important aspect in business, education, insurance, and other real-life situations. Many decisions are made by assigning probabilities to all possible outcomes pertaining to the situation and then evaluating the results. For instance, an insurance company might be able to assign probabilities to the number of vehicles a family owns. This information will help the company in making decisions regarding future situations. This involves random variables and probability distributions. Getting Ready
- 11. Larson & Farber, Elementary Statistics: Picturing the World, 3e 11
- 12. Larson & Farber, Elementary Statistics: Picturing the World, 3e 12 Discrete Probability Distributions A discrete probability distribution lists each possible value the random variable can assume, together with its probability. A probability distribution must satisfy the following conditions. In Words In Symbols 1. The probability of each value of the discrete random variable is between 0 and 1, inclusive. 0 P (x) 1 2. The sum of all the probabilities is 1. ΣP (x) = 1
- 13. Larson & Farber, Elementary Statistics: Picturing the World, 3e 13 Random Variables Example: Decide if the random variable x is discrete or continuous. a.) The distance your car travels on a tank of gas b.) The number of students in a statistics class The distance your car travels is a continuous random variable because it is a measurement that cannot be counted. (All measurements are continuous random variables.) The number of students is a discrete random variable because it can be counted.
- 14. Larson & Farber, Elementary Statistics: Picturing the World, 3e 14 Constructing a Discrete Probability Distribution Guidelines Let x be a discrete random variable with possible outcomes x1, x2, … , xn. 1. Make a frequency distribution for the possible outcomes. 2. Find the sum of the frequencies. 3. Find the probability of each possible outcome by dividing its frequency by the sum of the frequencies. 4. Check that each probability is between 0 and 1 and that the sum is 1.
- 15. Larson & Farber, Elementary Statistics: Picturing the World, 3e 15 Identifying Discrete Random Distribution DIRECTION: Identify whether the following distribution is a discrete probability distribution. Hint: The distribution should satisfy both of the properties. x 1 2 3 4 5 P(x) 0.10 0.20 0.25 0.40 0.05 x 1 2 3 4 5 P(x) 0.05 0.25 0.33 0.28 0.08
- 16. Larson & Farber, Elementary Statistics: Picturing the World, 3e 16 Identifying Discrete Random Distribution Hint: The distribution should satisfy both of the properties. x 1 2 3 4 5 P(x) 0.08 0.25 0.34 0.31 0.04 x 1 2 3 4 5 P(x) 0.03 0.22 1.01 0.23 0.02 x 1 2 3 4 5 P(x) 0.05 0.27 0.34 0.28 0.06
- 17. Larson & Farber, Elementary Statistics: Picturing the World, 3e 17 Challenge: Find P(3) Hint: Properties of a discrete random variable. x 0 1 2 3 4 P(x) 0.05 0.25 0.4 ? 0.06 x 0 1 2 3 4 P(x) 1/2 3/16 2/16 ? 1/16
- 18. Larson & Farber, Elementary Statistics: Picturing the World, 3e 18 WRAP IT UP! • What is a discrete probability distribution? • What are the symbols involved in discrete probability distribution? • What are the properties of a discrete probability distribution?