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Get rich A survey of 4826 randomly selected young adults (aged 19 to 25) asked, 鈥淲hat do you think are the chances you will have much more than a middle-class income at age 30?鈥 The two-way table shows the responses.

14 Choose a survey respondent at random.

(a) Given that the person selected is male, what鈥檚 the probability that he answered 鈥渁lmost certain鈥?

(b) If the person selected said 鈥渟ome chance but probably not,鈥 what鈥檚 the probability that the person is female?

Short Answer

Expert verified

Part (a) P (Almost certain/Male) =0.2428

Part (b) P (Female/some chance)=0.5983

Step by step solution

01

Part (a) Step 1. Given Information 

N=4826 young adults were chosen as part of the sample. The responses are organised in a two-way table.

02

Part (a) Step 2. Concept Used

Formula's used:P(A)=totalnumberofoutcomescorrespondingtoeventAnumberofoutcomesinsamplespace

03

Part (a) Step 3. Calculation

The selected person is a man, according to the inquiry. Now we must calculate the chance that the result for "nearly certain" is correct.

Therefore,P(AlmostcertainandMale)=favorableoutcomespossibleoutcomes=5974826

P(Male)=favorableoutcomespossibleoutcomes=24594826

As a result, the conditional probability is:

P(Almostcertain|Male)=P(AlmostcertainandMale)P(Male)P(Almostcertain|Male)=597482624594856P(Almostcertain|Male)=5972459P(Almostcertain|Male)0.2428

As a result, the likelihood of the result being "nearly definite" is

P(Almostcertain/Male)=0.2428

04

Part (b) Step 1. Calculation

The chosen person is female, according to the query. The next step is to calculate the probability that the result for "some chance but probability not" is correct. Therefore,

P(Femaleandsomechance)=favorableoutcomespossibleoutcomes=4264826

P(somechance)=favorableoutcomespossibleoutcomes=7124826

As a result, the conditional probability is:

P(Female/somechance)=P(Femaleandsomechance)P(Female)P(Female/somechance)=42648267124826P(Female/somechance)=426712P(Female/somechance)0.5983

As a result, the probability that the result for "some chance but probability not" is "some chance but probability not" is P(Female/somechance)=0.5983

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