Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
4. Probability
Basic Concepts of Probability
Problem 5.1.18b
Textbook Question
Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).

Using Probabilities for Significant Events
b. Find the probability of getting 2 or more matches.

1
Step 1: Understand the problem. We are tasked with finding the probability of getting 2 or more matches in the California Daily 4 lottery. This means we need to calculate the sum of probabilities for x = 2, x = 3, and x = 4.
Step 2: Refer to the provided table. The table lists the probabilities for different numbers of matching digits (x). Specifically, P(x=2) = 0.049, P(x=3) = 0.004, and P(x=4) = 0+.
Step 3: Add the probabilities for x = 2, x = 3, and x = 4. Use the formula: \( P(x \geq 2) = P(x=2) + P(x=3) + P(x=4) \). Substitute the values from the table into this formula.
Step 4: Perform the addition. Combine the probabilities: \( P(x \geq 2) = 0.049 + 0.004 + 0+ \). Note that the probability for x = 4 is effectively zero (0+).
Step 5: Interpret the result. The sum represents the probability of getting 2 or more matches in the lottery. This is the final probability value, which can be used to understand the likelihood of this event occurring.

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