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Chapter 11: Problem 78

Write a probability problem involving the word "and" whose solution results in the probability fractions shown. \(\frac{1}{6} \cdot \frac{1}{6} \cdot \frac{1}{6}\)

Short Answer

Expert verified
A problem that fits the description is: 'What is the probability of rolling a 1 on a fair six-sided die three times in a row?'. This specific scenario results in the probability fractions \( \frac{1}{6} \cdot \frac{1}{6} \cdot \frac{1}{6} \).

Step by step solution

01

Frame a Situation

First, consider a context that involves the occurrence of three successive events, each of which has a probability of \( \frac{1}{6} \). The canonical example of such a situation is rolling a fair six-sided die three times in a row and having a specific outcome each roll.
02

Define the Probability

In the case of a fair six-sided die, the probability of rolling any given number (say 1) is \( \frac{1}{6} \). Let's imagine we want the outcome of each roll to be 1.
03

Calculate the Combined Probability

To calculate the combined probability, multiply the individual probabilities. So, the probability of rolling a 1 on three consecutive rolls of a fair six-sided die is \( \frac{1}{6} \cdot \frac{1}{6} \cdot \frac{1}{6} \).

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Most popular questions from this chapter

We return to our box of chocolates. There are 30 chocolates in the box, all identically shaped. Five are filled with coconut, 10 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting two caramel-filled chocolates in a row.

Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. I found the probability of getting rain at least once in ten days by calculating the probability that none of the days have rain and subtracting this probability from \(1 .\)

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