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. Female Male Total Almost no chance 9698194 Some chance but probably not 426286712 A 50-50 chance 6967201416 A good chance 6637581421 Almost certain 4865971083 Total 236724594826 Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Find P(C∣M). Interpret this value in context.

Question

A survey of 4826 randomly selected young adults (aged 19 to 25) asked, &quot;What do you think are the chances you will have much more than a middle-class income at age 30?&quot; The two-way table summarizes the responses.  Female  Male  Total  Almost no chance 9698194 Some chance but   probably not 426286712 A 50-50 chance 6967201416 A good chance 6637581421 Almost certain 4865971083 Total 236724594826 Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Find P(C∣M). Interpret this value in context.

avortarF · Accepted Answer

Definitions  Definition conditional probability:  P(B|A)=P(A∩B)P(A)=P(A and B)P(A)  SOLUTION   Female  Male  Total  Almost no chance 9698194 Some chance but   probably not 426286712 A 50-50 chance 6967201416 A good chance 6637581421 Almost certain 4865971083 Total 236724594826  G=Good chance  M=Male  We note that the table contains information about 4826 young adults (given in the bottom right corner of the table).  Moreover, 2459 of the 4826 young adults are male, becatise 2450 is mentioned in the row &quot;Total” and in the column ”Male” of the table.  The probability is the number of favorable outcomes divided by the number of possible outcomes:  P(M)=# of favorable outcomesof possible outcomes=24594826  Next, we note that. 758 of the 4826 children are from England and prefer Telepathy, because 758 is mentioned in the row ”A good chance” and in the column &quot;Male” of the given table.  P(GandM)=# of favorable outcomesof possible outcomes=7584826  Use the definition of conditional probability:  P(G|M)=P(GandM)P(M)=758482624594826=7582459≈0.3083=30.83%  30.83% of the male young adults think there is a good chance that they will have much more than a middle-class income at age 30.  7582459≈0.3083=30.83%

A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do you think

Answered question

Answer & Explanation

New Questions in College Statistics