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A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do you think are the chances you will have much more than a middle-class income at age 30?" The two-way table summarizes the responses. Choose a survey respondent at random. Define events G: good chance, M: male, and N: almost no chance. Opinion Almost no chance Some chance but probably not A 50-50 chance A good chance Almost certain Total Gender 96 Female Male Total 98 194 712 720 1416 426 286 696 663 758 1421 486 597 1083 2367 2459 4826 Given that the chosen survey respondent didn't say "almost no chance," what's the probability that this person is female? Write your answer as a probability statement using correct symbols for the events. OP (MC | NC) = 426+696+663+486 4826 = 0.471 O P (MC | NC) = 4826-96-98 = 0.960 4826 OP (NC | MC) P(MN): = OP (MC INC) = 98 194 = = = 0.505 = 4632 4826 426+696+663+486 2271 2367 2367 2271 4826 = 426+696+663+486 712+1416+1421+1083 = = 0.959 2271 4632 = 0.490

A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do you think are the chances you will have much more than a middle-class income at age 30?" The two-way table summarizes the responses. Choose a survey respondent at random. Define events G: good chance, M: male, and N: almost no chance. Opinion Almost no chance Some chance but probably not A 50-50 chance A good chance Almost certain Total Gender 96 Female Male Total 98 194 712 720 1416 426 286 696 663 758 1421 486 597 1083 2367 2459 4826 Given that the chosen survey respondent didn't say "almost no chance," what's the probability that this person is female? Write your answer as a probability statement using correct symbols for the events. OP (MC | NC) = 426+696+663+486 4826 = 0.471 O P (MC | NC) = 4826-96-98 = 0.960 4826 OP (NC | MC) P(MN): = OP (MC INC) = 98 194 = = = 0.505 = 4632 4826 426+696+663+486 2271 2367 2367 2271 4826 = 426+696+663+486 712+1416+1421+1083 = = 0.959 2271 4632 = 0.490

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Survey Overview A survey of 4,826 randomly selected young adults (aged 19 to 25) was conducted to assess their perceptions about the likelihood of earning much more than a middle-class income by age 30. The table below summarizes the responses based on gender and opinion regarding their chances. #### Two-Way Table: Gender and Opinion | Opinion | Female | Male | Total | |-------------------------------|--------|------|-------| | Almost no chance | 96 | 98 | 194 | | Some chance but probably not | 426 | 286 | 712 | | A 50-50 chance | 696 | 720 | 1416 | | A good chance | 663 | 758 | 1421 | | Almost certain | 486 | 597 | 1083 | | **Total** | 2367 | 2459 | 4826 | **Definitions:** - \( G \): Good chance - \( M \): Male - \( N \): Almost no chance ### Probability Problem The task is to calculate the probability that a randomly selected respondent is female given they did not respond with "almost no chance." **Calculations:** To find the probability \( P(M^C | N^C) \): - Total respondents that did not say "almost no chance" \( N^C \): - \( 4826 - 194 = 4632 \) - Female respondents that did not say "almost no chance": - \( 426 + 696 + 663 + 486 = 2271 \) - \( P(M^C | N^C) = \frac{2271}{4632} \approx 0.490 \) ### Options Evaluated 1. **\( P(M^C | N^C) = \frac{2271}{4826} = 0.471 \)** 2. **\( P(M^C | N^C) = \frac{4632}{4826} = 0.960 \)** 3. **\( \mathbf{P(M^C | N^C) = \frac{2271}{2367} = 0.959} \)** 4. **\( P(M | N) = \frac{98}{194} =
Transcribed Image Text:### Survey Overview A survey of 4,826 randomly selected young adults (aged 19 to 25) was conducted to assess their perceptions about the likelihood of earning much more than a middle-class income by age 30. The table below summarizes the responses based on gender and opinion regarding their chances. #### Two-Way Table: Gender and Opinion | Opinion | Female | Male | Total | |-------------------------------|--------|------|-------| | Almost no chance | 96 | 98 | 194 | | Some chance but probably not | 426 | 286 | 712 | | A 50-50 chance | 696 | 720 | 1416 | | A good chance | 663 | 758 | 1421 | | Almost certain | 486 | 597 | 1083 | | **Total** | 2367 | 2459 | 4826 | **Definitions:** - \( G \): Good chance - \( M \): Male - \( N \): Almost no chance ### Probability Problem The task is to calculate the probability that a randomly selected respondent is female given they did not respond with "almost no chance." **Calculations:** To find the probability \( P(M^C | N^C) \): - Total respondents that did not say "almost no chance" \( N^C \): - \( 4826 - 194 = 4632 \) - Female respondents that did not say "almost no chance": - \( 426 + 696 + 663 + 486 = 2271 \) - \( P(M^C | N^C) = \frac{2271}{4632} \approx 0.490 \) ### Options Evaluated 1. **\( P(M^C | N^C) = \frac{2271}{4826} = 0.471 \)** 2. **\( P(M^C | N^C) = \frac{4632}{4826} = 0.960 \)** 3. **\( \mathbf{P(M^C | N^C) = \frac{2271}{2367} = 0.959} \)** 4. **\( P(M | N) = \frac{98}{194} =
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