Question 467339
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The other tutor's solution is incorrect.

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In a group of 20 person, 5 are females. If 3 persons are picked out of 20 at random, what is the probability that they all are females?
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 There are C(5,3) ways to pick a group of 3 females out of the 5.

There are C(20,3) ways to pick any group of 3 persons

So the probability is {{{C(5,3)/C(20,3)= 10/1140 = 1/114}}}

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What is the probability of atleast one being female?
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We find the probability of the complement event and subtract
from 1.

The complement event of at least one female is having no females
which means all males.

Since there are 5 females, there are 15 males.

So there are C(15,3) ways to pick a group of 3 males out of the 15.

There are C(20,3) ways to pick any group of 3 persons

So the probability is {{{C(15,3)/C(20,3)= 455/1140 = 91/228}}}

Edwin</pre>