Question

PROBABILITY. Archibald Haddock is arrested in Borduria and has a trial. The jury system in Borduria is somewhat different than ours, where lawyers interview perspective jurors and select 12. In Borduria, the judge calls in 6 professors from the nearby college faculty and 8 idiots from the street. The runner-up in the Miss Borduria beauty pageant randomly picks 6 of these 14 people for the jury. What is the probability that the jury will be 3 professors and 3 idiots? What is the probability that the jury will be 1 professor and 5 idiots? Bonus points. Who is Archibald Haddock? (without Googling his name, honor system) Where is Borduria?

Answer 1

Number of ways to picks 6 of 14 people for the jury =

= 14! / (8! * 6!) = 3003

Number of ways to picks 3 of 6 professors for the jury =

= 6! / (3! * 3!) = 20

Number of ways to picks 3 of 8 idiots for the jury =

= 8! / (5! * 3!) = 56

Probability that the jury will be 3 professors and 3 idiots = (Number of ways to picks 3 of 6 professors for the jury * Number of ways to picks 3 of 8 idiots for the jury ) / Number of ways to picks 6 of 14 people for the jury

= (20 * 56) / 3003

= 0.3729604

Number of ways to picks 1 of 6 professors for the jury =

= 6! / (5! * 1!) = 6

Number of ways to picks 5 of 8 idiots for the jury =

= 8! / (3! * 5!) = 56

Probability that the jury will be 1 professors and 5 idiots = (Number of ways to picks 1 of 6 professors for the jury * Number of ways to picks 5 of 8 idiots for the jury ) / Number of ways to picks 6 of 14 people for the jury

= (1 * 56) / 3003

= 0.01864802