SOLUTION: In one town, 35% of adults are employed in the tourism industry. What is the probability that three adults selected at random from the town are all employed in the tourism industry

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Question 1135163: In one town, 35% of adults are employed in the tourism industry. What is the probability that three adults selected at random from the town are all employed in the tourism industry?

Found 3 solutions by mathsolverplus, greenestamps, ikleyn:
Answer by mathsolverplus(88)   (Show Source): You can put this solution on YOUR website!
Let's say there are 100 adults in the town and 35 of them work for the tourism industry.
The chance of selecting one adult will be 35/100.
The chance of selecting another adult will be 34/99.
(Since we removed one adult already, we need to subtract 1 from both numerator and denominator)
The chance of selecting the third adult will be 33/98.

Probability of three adults being selected:
=(35/100)(34/99)(33/98)
=0.04047619047






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Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


The solution by tutor @mathsolverplus is incorrect.

The probability that each of the three adults selected is employed in the tourism industry does not change each time one of the adults is selected; the probability for each one is 35%.

P(all three are employed in tourism industry) = (0.35)^3 = .042875
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.
Since in this problem the number of adults in the city IS NOT SPECIFIED, we only can assume by default that this number is VERY LARGE.


    And it is THE ONLY WAY on how we can treat/interpret the condition.


All what we know (and what is given to us) in this problem is that the probability for randomly selected adult to be employed 
in the tourism industry is 0.35.


At this context and under given condition, the solution to the problem and the ANSWER is   = 0.042875.



Interpretation given and used by @mathsolverplus in his post is incorrect and non-adequate.

--------------

It is just, probably, couple of weeks I observe an activity of @mathsolverplus at this forum.

Regarding this activity, I can resume that for routine problems @mathsolverplus, probably, can provide valid solutions
(although not always).

But for the problems "one step away from routine" the probability he provides incorrect answers becomes dangerously high.

Under supervision and correction from other tutors in this forum, it still can be kept in some reasonable frames
(although, I personally am not very happy to clean after him . . . ).

But as a self-standing tutor at his own web-site, without supervising and corrections from other tutors he is not able
to provide error-proven (error-free) solutions on stable basis.

Keep it in your mind if/when you will consider to follow him at his web-sites.

You will be at constant risk of getting wrong solutions.


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