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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 3.2.20

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.

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Step 1: Understand the problem. We are tasked with finding the probability of two independent events occurring in sequence: tossing a tail on a coin and rolling a number greater than 2 on a die.
Step 2: Recall the Multiplication Rule for independent events. The probability of two independent events A and B occurring is given by P(A and B) = P(A) × P(B).
Step 3: Determine the probability of the first event (tossing a tail). A fair coin has two sides (head and tail), so the probability of tossing a tail is P(Tail) = 1/2.
Step 4: Determine the probability of the second event (rolling a number greater than 2). A standard die has six faces numbered 1 through 6. The numbers greater than 2 are 3, 4, 5, and 6, which is 4 outcomes out of 6. Therefore, P(Number > 2) = 4/6 = 2/3.
Step 5: Apply the Multiplication Rule. Multiply the probabilities of the two events: P(Tail and Number > 2) = P(Tail) × P(Number > 2). Substitute the values P(Tail) = 1/2 and P(Number > 2) = 2/3 into the formula to find the final probability.

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Multiplication Rule of Probability

The Multiplication Rule states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the events are tossing a coin and rolling a die, which do not affect each other. This rule is essential for calculating the combined probability of multiple events.
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Probability of Multiple Independent Events

Independent Events

Independent events are those whose outcomes do not influence one another. For example, the result of tossing a coin does not affect the outcome of rolling a die. Understanding that these events are independent is crucial for applying the Multiplication Rule correctly in probability calculations.
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Probability of Multiple Independent Events

Calculating Probabilities

Calculating probabilities involves determining the likelihood of specific outcomes. For the coin toss, the probability of getting a tail is 1/2, while for the die, the probability of rolling a number greater than 2 (i.e., 3, 4, 5, or 6) is 4/6. Knowing how to compute these probabilities is vital for solving the problem.
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Probability From Given Z-Scores - TI-84 (CE) Calculator
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