4. Probability
Basic Concepts of Probability
1:24 minutesProblem 5.1.19a
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
a. Find the probability of getting exactly 3 matches.
Verified step by step guidance1
Step 1: Understand the problem. The goal is to find the probability of getting exactly 3 matches in the California Daily 4 lottery. The table provided lists the probabilities for different numbers of matching digits (x).
Step 2: Locate the relevant probability in the table. The table shows the probability P(x) for each number of matching digits. For x = 3 (exactly 3 matches), the corresponding probability is 0.004.
Step 3: Interpret the probability. The value 0.004 represents the likelihood of selecting 3 digits that match the drawn digits in the same order during a 'straight' bet.
Step 4: Verify the context. Ensure that the table and problem description align with the calculation. The table explicitly provides the probability for x = 3, so no further computation is needed.
Step 5: Conclude the process. The probability of getting exactly 3 matches is directly obtained from the table as 0.004. This concludes the solution process.
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