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

permaneceerc 2021-01-19 Answered
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. Given that the chosen student didnt
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Expert Answer

Bertha Stark
Answered 2021-01-20 Author has 96 answers

Definitions
Complement rule
P(Ac)=P(not A)=1P(A)
Definition conditional probability:
P(BorA)=P(AB)P(A)=P(AandB)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
N=Almost no chance
M=Male
We note that the table contains information about 4826 young adults (given in the bottom right corner of the table).
Moreover, 194 of the 4826 young adults have the opinion "Almost no chance” because 194 is mentioned in the row ” Almost no chance” and in the column "Total " of the table. This then implies that 4826194=4632 young adults do not have the opinion of "Almost no chance"
The probability is the number of favorable outcomes divided by the number of possible outcomes:
P(Nc)=# of favorable outcomesof possible outcomes=46324826
Next, we note that 96 of the 4826 young adults are female and have the opinion ” Almost no chance”, because 96 is mentioned in the row ” Almost no chance” and in the column *Female” of the given table. Since there are 2367 females, 236796=2271 of the 4826 young adults did not have the opinion ” Almost no chance.” P(McandNc)=# of favorable outcomesof possible outcomes=22714826
Use the definition of conditional probability:
P(Mc|Nc)=P(McandNc)P(Nc)=2271482646324826=22714632=75715440.4903=49.03%
Result 75715440.4903=49.03%

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