Problem Solving

In a survey for 248 people,156 are married,70 are self employed and 25 percent of those who married are self employed.if a person is to be randomly selected from those sureveyed.what is the probability that the person selected will be self employed but not married ?

Ans. 1/8

Need explanation pls.

Gopaleie2k4 wrote:In a survey for 248 people,156 are married,70 are self employed and 25 percent of those who married are self employed.if a person is to be randomly selected from those sureveyed.what is the probability that the person selected will be self employed but not married ?

Ans. 1/8

Need explanation pls.

total people = 248
Married (selfemployed + not selfemployed) = 156
25% of married are selfemployed, so this number is (25/100)*156 =39
self employed people total = 70
so self employed people who are not married = 70-39 = 31
Required probability = 31/248 = 1/8

We can use a table to organize information given in otherwise confusing overlapping problem sets. We just carefully fill in the chart with the info.



---------------------self employed-------not self employed--------total
married---------------39----------------------------------------------156
not married-----------31-------------------------------------------------
total-------------------70---------------------------------------------------


We are told :25 percent of those who married are self employed. Thus,
156* 1/4 = 39. We can easily find out those not married and self employed by subtracting the total of those self employed from those that are married. This gives us 31.

So the
probability that the person selected will be self employed but not married = 31/248 = 1/8

I drew Venn Diagram..Hope it helps !!!!!

I got confused when trying to find the probability because I thought that you had to find the probability that the person chosen would be 1st not married AND self employed.

So I did the following

(not married/total) * (self employed/total not married)
which is the same as (92/248) * 31/92)

I didn't know that I could just put self employed/total

Can you please expalin