Probability Word Problem

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HopeDip

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Hello! I have homework due by midnight tonight, and I am having trouble with a word problem. This is the practice version.

Three hundred people apply for three jobs. 80 of the applicants are women.
If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)

I was able to figure out the first part of the problem, which was figuring the probability of all the selected people being women. Please help! I am trying to figure this out from my textbook or searching but either my brain is stupid or I everything is really cryptic because I am stumped. Thanks!
 
HopeDip said:
Hello! I have homework due by midnight tonight, and I am having trouble with a word problem. This is the practice version.

Three hundred people apply for three jobs. 80 of the applicants are women.
If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)

I was able to figure out the first part of the problem, which was figuring the probability of all the selected people being women. Please help! I am trying to figure this out from my textbook or searching but either my brain is stupid or I everything is really cryptic because I am stumped. Thanks!
Click to expand...
What answer did you get for the "probability"? (I assume that's the first part you are referencing here)
 
If three persons are selected at random, what is the probability that one is a woman?
Exactly one is a woman or at least one is a woman? Big difference.
 
sky2rain said:
If exactly one, ( c(240,1)*c(60,2))/c(300,3)
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Did you misread 80 as 60?

HopeDip said:
Hello! I have homework due by midnight tonight, and I am having trouble with a word problem. This is the practice version.

Three hundred people apply for three jobs. 80 of the applicants are women.
If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)

I was able to figure out the first part of the problem, which was figuring the probability of all the selected people being women. Please help! I am trying to figure this out from my textbook or searching but either my brain is stupid or I everything is really cryptic because I am stumped. Thanks!
Click to expand...
If "one" means "at least one", then you can turn your attention to "none", which is the complement. This will be similar to the "all" case you have already solved.
 
Dr.Peterson said:
Did you misread 80 as 60?


If "one" means "at least one", then you can turn your attention to "none", which is the complement. This will be similar to the "all" case you have already solved.
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I thought 80% are women
 
JeffM said:
No that is the probability that no, two, or three women are chosen.
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The total probability is the sum of no, 1, 2 and 3 women are chosen, and that is 1. If 1 - the prob of no woman is chosen, then it’s the probability of at least 1 chosen, right?
 
sky2rain said:
The total probability is the sum of no, 1, 2 and 3 women are chosen, and that is 1. If 1 - the prob of no woman is chosen, then it’s the probability of at least 1 chosen, right?
Click to expand...
Yes, I misread your post #8.
 
Jomo said:
Why are giving the student the answer? Please read the forum's posting guidelines.
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To be honest I have trouble understanding what he’s asking… it seems that he thinks all whom are selected are women… so it seems a problem of understanding the problem in English.
 
sky2rain said:
To be honest I have trouble understanding what he’s asking… it seems that he thinks all whom are selected are women… so it seems a problem of understanding the problem in English.
Click to expand...
As I understand it, it was a two-part problem, and we were not directly shown the first part:
HopeDip said:
Hello! I have homework due by midnight tonight, and I am having trouble with a word problem. This is the practice version.

Three hundred people apply for three jobs. 80 of the applicants are women.
If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)

I was able to figure out the first part of the problem, which was figuring the probability of all the selected people being women. Please help! I am trying to figure this out from my textbook or searching but either my brain is stupid or I everything is really cryptic because I am stumped. Thanks!
Click to expand...
So it was probably something like:

(a) What is the probability that all the selected people are women?​
(b) What is the probability that one is a woman?​

The problem we have is that it is not written (or copied) clearly, as "one" could mean "exactly one" or "at least one". We can't tell where the OP is having trouble, because we haven't been told. And we never will be.
 
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