Understanding Basic St.. Welcome to RedShelf eReader! Just getting started? Head over to our partner support page for a guide on the basics. Q| 247 GUIDED EXERCISE 3 EXPECTED VALUE At a carnival, you pay $2.00 to play a coin-flipping game with three fair coins. On each coin, one side has the num- ber 0 and the other side has the number 1. You flip the three coins at one time and you win $1.00 for every 1 that appears on top. Are your expected earnings equal to the cost to play? We'll answer this question in several steps. (a) In this game, the random variable of interest counts the number of 1's that show. What is the sample space for the values of this random variable? The sample space is {0, 1, 2, 3}, since any of these num- bers of 1's can appear. (b) There are eight equally likely outcomes for throw- ing three coins. They are 000, 001, 010, 011, 100, 101, 110 and 111. and (c) Complete Table 6-6. TABLE 6-6 TABLE 6-7 Completion of Table 6-6 Number of 1's, Number of 1's, Frequency P(x) xP(x) Frequency P(x) XP(x) 1 0.125 1 0.125 0. 1 0.375 1 0.375 0.375 3. 0.375 0.750 1 0.125 0.375 Focus Page 2 of 3 229 words English (United States) 909 AT MAR átv S 23 2. 3. me tỏ RedShelf eReader! Just getting started? Head over to our partner support page for a guide on the basics. There are eight equally likely outcomes for throw- ing three coins. They are 000, 001,010, 011, 100, 101, 247 110 and 111. and (c) Complete Table 6-6. TABLE 6-6 TABLE 6-7 Completion of Table 6-6 Number of 1's, Number of 1's, х Frequency P(x) xP(x) Frequency P(x) xP(x) х 1 0.125 1 0.125 0. 0.375 1 3 0.375 0.375 0.375 0.750 1 0.125 0.375 The expected value can be found by summing the last column of Table 6-7. The expected value is $1.50. It cost $2.00 to play the game; the expected value is less than the cost. The carnival is making money. In the long run, the carnival can expect to make an average of about 50 cents per player. (d) The expected value is the sum μ = ΣΧΡ(x) Sum the appropriate column of Table 6-6 to find this value. Are your expected earnings less than, equal to, or more than the cost of the game? Focus Page 2 of 3 229 words 4X English (United States) 909 P\

Understanding Basic St.. Welcome to RedShelf eReader! Just getting started? Head over to our partner support page for a guide on the basics. Q| 247 GUIDED EXERCISE 3 EXPECTED VALUE At a carnival, you pay $2.00 to play a coin-flipping game with three fair coins. On each coin, one side has the num- ber 0 and the other side has the number 1. You flip the three coins at one time and you win $1.00 for every 1 that appears on top. Are your expected earnings equal to the cost to play? We'll answer this question in several steps. (a) In this game, the random variable of interest counts the number of 1's that show. What is the sample space for the values of this random variable? The sample space is {0, 1, 2, 3}, since any of these num- bers of 1's can appear. (b) There are eight equally likely outcomes for throw- ing three coins. They are 000, 001, 010, 011, 100, 101, 110 and 111. and (c) Complete Table 6-6. TABLE 6-6 TABLE 6-7 Completion of Table 6-6 Number of 1's, Number of 1's, Frequency P(x) xP(x) Frequency P(x) XP(x) 1 0.125 1 0.125 0. 1 0.375 1 0.375 0.375 3. 0.375 0.750 1 0.125 0.375 Focus Page 2 of 3 229 words English (United States) 909 AT MAR átv S 23 2. 3. me tỏ RedShelf eReader! Just getting started? Head over to our partner support page for a guide on the basics. There are eight equally likely outcomes for throw- ing three coins. They are 000, 001,010, 011, 100, 101, 247 110 and 111. and (c) Complete Table 6-6. TABLE 6-6 TABLE 6-7 Completion of Table 6-6 Number of 1's, Number of 1's, х Frequency P(x) xP(x) Frequency P(x) xP(x) х 1 0.125 1 0.125 0. 0.375 1 3 0.375 0.375 0.375 0.750 1 0.125 0.375 The expected value can be found by summing the last column of Table 6-7. The expected value is $1.50. It cost $2.00 to play the game; the expected value is less than the cost. The carnival is making money. In the long run, the carnival can expect to make an average of about 50 cents per player. (d) The expected value is the sum μ = ΣΧΡ(x) Sum the appropriate column of Table 6-6 to find this value. Are your expected earnings less than, equal to, or more than the cost of the game? Focus Page 2 of 3 229 words 4X English (United States) 909 P\

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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