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Chapter 4: Problem 46

How many different outcomes are possible for 10 tosses of a coin?

Short Answer

Expert verified
The total number of different outcomes possible for 10 tosses of a coin is 1024.

Step by step solution

01

Identify the base of possible outcomes per event

For a single coin toss, there are two possible outcomes: heads or tails.
02

Identify the number of events

The number of coin tosses is 10. Each toss of the coin is considered an individual event.
03

Apply the principle of multiplication

The total number of outcomes for multiple events is found by multiplying the number of outcomes of each individual event. In this case, each toss has two outcomes and there are 10 events (10 tosses), so the total number of outcomes is \(2^{10}\).
04

Calculate the total number of outcomes

By calculating \(2^{10}\), we find the total number of possible outcomes is 1024.

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Most popular questions from this chapter

Explain the meaning of the intersection of two events. Give one example.

Of a total of 100 CDs manufactured on two machines, 20 are defective. Sixty of the total CDs were manufactured on Machine \(I\), and 10 of these 60 are defective. Are the events "machine type" and "defective CDs" independent? (Note: Compare this exercise with Example 4-20.)

Given that \(A\) and \(B\) are two mutually exclusive events, find \(P(A\) or \(B\) ) for the following. a. \(P(A)=.25\) and \(P(B)=.27\) b. \(P(A)=.58\) and \(P(B)=.09\)

Suppose that \(20 \%\) of all adults in a small town live alone, and \(8 \%\) of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?

The probability is \(.80\) that a senior from a large college in New York State has never gone to Florida for spring break. If two college seniors are selected at random from this college, what is the probability that the first has never gone to Florida for spring break and the second has? Draw a tree diagram for this problem.
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