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A meeting takes place between a diplomat and seventeen government officials. However, ten of the officials are actually spies.
The diplomat gives secret information to six of the attendees. Find the following probabilities. Enter your answer as a percent,
rounded to the nearest thousandth.
a) What is the probability that the diplomat gave secret information to exactly six spies?
In all, there are 
ways to select a group of 6 from 17 officials. - It is the measure of your space of events.
And there are 
ways to make a group of 6 from 10 spies.
So, the answer to the problem question in this case is 
.
I do not go into further calculations, since you (as I assume from your post) know how to do it.
b) What is the probability that the half of the attendees who got the secret information were spies?
In other words, what is the probability that 3 of the 6 attendees who got the secret information were spies?
Follow the same logic. You will get the answer 
.
c) What is the probability that the diplomat gave secret information to exactly one spy?
.
d) What is the probability that no spies have got the secret information?
This time you construct the numerator as 
= 
, where 7 = 17-10 is the number of loyal officials,
and your final answer is 
.
e) What is the probability that the diplomat gave secret information to at least one spy?
This probability is the COMPLEMENT to the probability of the part d), i.e. 1 - .
Solved - all questions are answered and explained.
