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Chapter 4: Problem 24

Four coins are tossed. How many simple events are in the sample space?

Short Answer

Expert verified
Answer: There are 16 simple events in the sample space when four coins are tossed.

Step by step solution

01

Understand the problem and possible outcomes of each coin

Tossing four coins will have four independent events that could result in a head or tail. For each coin, there are two possible outcomes: heads (H) or tails (T).
02

Use the multiplication principle to find the number of simple events in the sample space

The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m*n ways to do both. Since there are two outcomes for each coin and four coins in total, we can use the multiplication principle to find the total number of simple events in the sample space. To calculate, we multiply the number of outcomes for each coin: 2 (outcomes for coin 1) * 2 (outcomes for coin 2) * 2 (outcomes for coin 3) * 2 (outcomes for coin 4)
03

Calculate the total number of simple events

Multiply the outcomes of each coin to determine the total number of simple events in the sample space: 2 * 2 * 2 * 2 = 16 There are 16 simple events in the sample space when four coins are tossed.

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Most popular questions from this chapter

A key ring contains four office keys that are identical in appearance, but only one will open your office door. Suppose you randomly select one key and try it. If it does not fit, you randomly select one of the three remaining keys. If it does not fit, you randomly select one of the last two. Each different sequence that could occur in selecting the keys represents one of a set of equiprobable simple events. a. List the simple events in \(S\) and assign probabilities to the simple events. b. Let \(x\) equal the number of keys that you try before you find the one that opens the door \((x=1,2,3,4)\). Then assign the appropriate value of \(x\) to each simple event. c. Calculate the values of \(p(x)\) and display them in a table. d. Construct a probability histogram for \(p(x)\).

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