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# Probability question

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Why bother with a post grad course - waste of time? 17-10-2016
1. I'm completely stuck on this question and I'm pretty sure my answers are wrong. Any help would be much appreciated!!

Undergraduate economists can either do a single Honours degree
or a joint Honours degree. Their society has a party which they all
attend. They are joined by other joint Honours students who are not
doing any economics at all. 55% of people are doing a joint Honours
degree and 65% of people are doing some economics. 100 people
attend the party.

a) What is the probability that a single Honours student at the party is
also doing economics?

b) What is the probability that an economist is a single Honours
student?

c) What is the probability that a joint Honours student is studying
economics?

d) What are the odds that a student is a joint Honours economist?

e) Five joint honours students leave the room. What is the probability
that they are a mixed group of economists and non-economists?
2. (Original post by JellyCat99)
I'm completely stuck on this question and I'm pretty sure my answers are wrong. Any help would be much appreciated!!

Undergraduate economists can either do a single Honours degree
or a joint Honours degree. Their society has a party which they all
attend. They are joined by other joint Honours students who are not
doing any economics at all. 55% of people are doing a joint Honours
degree and 65% of people are doing some economics. 100 people
attend the party.

a) What is the probability that a single Honours student at the party is
also doing economics?

b) What is the probability that an economist is a single Honours
student?

c) What is the probability that a joint Honours student is studying
economics?

d) What are the odds that a student is a joint Honours economist?

e) Five joint honours students leave the room. What is the probability
that they are a mixed group of economists and non-economists?
Draw a Venn Diagram and introduce some unknowns to represent proportions that you haven't been given, and use algebra to find them. Then use Bayes' Theorem to find the probabilities, noting that e.g. "What is the probability that a single Honours student at the party is also doing economics?" can be rewritten as "What is the probability that a student is doing economics, given that they are a single Honours student?"

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