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Chapter 4: Problem 83

How many different outcomes are possible for four rolls of a die?

Short Answer

Expert verified
There are 1296 possible outcomes for four rolls of a die.

Step by step solution

01

Understand the Problem

A die has six faces, so each time you roll the die, there are six possible outcomes. Because each roll is independent, the number of outcomes for each roll stays the same - it is always six.
02

Calculate the Number of Outcomes for One Roll

A die has six faces, so there are six possible outcomes for each roll.
03

Calculate the Number of Outcomes for Four Rolls

Since each roll is independent, the number of outcomes for four rolls is simply the number of outcomes for one roll, raised to the power of four. In our case, we have \(6^4\), which equals 1296.

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Most popular questions from this chapter

A car rental agency currently has 44 cars available, 28 of which have a GPS navigation system. One of the 44 cars is selected at random. Find the probability that this car a. has a GPS navigation system b. does not have a GPS navigation system

An economist says that the probability is \(.47\) that a randomly selected adult is in favor of keeping the Social Security system as it is, \(.32\) that this adult is in favor of totally abolishing the Social Security system, and .21 that this adult does not have any opinion or is in favor of other options. Were these probabilities obtained using the classical approach, relative frequency approach, or the subjective probability approach? Explain your answer.

Given that \(P(A \mid B)=.44\) and \(P(A\) and \(B)=.33\), find \(P(B)\).

A box contains 10 red marbles and 10 green marbles. a. Sampling at random from this box five times with replacement, you have drawn a red marble all five times. What is the probability of drawing a red marble the sixth time? b. Sampling at random from this box five times without replacement, you have drawn a red marble all five times. Without replacing any of the marbles, what is the probability of drawing a red marble the sixth time? c. You have tossed a fair coin five times and have obtained heads all five times. A friend argues that according to the law of averages, a tail is due to occur and, hence, the probability of obtaining a head on the sixth toss is less than \(.50\). Is he right? Is coin tossing mathematically equivalent to the procedure mentioned in part a or the procedure mentioned in part \(\mathrm{b}\) above? Explain.

In a group of adults, some own iPads, and others do not. If two adults are randomly selected from this group, how many total outcomes are possible? Draw a tree diagram for this experiment.
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