1/ At some point in a trial, the judge is 60% confident the suspect is guilty. T

Question

1/ At some point in a trial, the judge is 60% confident the suspect is guilty. The prosecutor brings an evidence showing that the criminal was left-handed. The suspect is also left-handed. If 20% of people are left-handed, how confident the judge about the suspect being guilty, after this evidence?

2/ Suppose that an urn has r red balls and b black balls. A ball is drawn and its color is noted. Then that ball is return to the urn, together with additional c balls of the same color as the drawn ball (for a given c > 0). Now another ball is drawn from the urn. Find the probability that this ball is red. Suppose this procedure is repeated n times. After that, an (n + 1)th ball is drawn. Find the probability pn+1 that this ball is red. [Hint: follow these steps:

i. You have computed p2 in part a. Guess a formula for pn+1. If necessary, compute p3 as well.

ii. Prove your guess by induction: suppose that the procedure is repeated n 1 times. How many balls are in the urn now? Assume that your guess is correct for pn. Now let the procedure be repeated one more time: compute pn+1 and show that your guess is correct for pn+1.

Explanation / Answer

Doing the first question only. Please repost the others

P( G)=0.60

P(L/G)=1

P(G/L) = p ( To be found out)

P(L) = P( L/G) * P(G) + P( L/G') * P(G')

P(L) = 0.60*1 + 0.20* 0.40=0.68

P( G/L) = P( G and L)/P(L) = 0.60/0.68 = 0.8823

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.