SOLUTION: 1. Suppose each of two shoe boxes contains a mixture of black-and-white marbles. One of the two boxes is to be chosen at random and a marble chosen at random from that box. Let A=

Question 838980: 1. Suppose each of two shoe boxes contains a mixture of black-and-white marbles. One of the two boxes is to be chosen at random and a marble chosen at random from that box. Let A= the event that box 1 is selected; Let B+ the even that box 2 is selected; C= the event that a black marble is drawn; D= the event that a white marble is drawn.
a. suppose box 1 contains 12 black and 8 white marbles, and box 2 contains 15 black and 10 white marbles. Show that A and D are independent.
b. suppose box 1 contains 8 black marbles and 2 white marbles, and box 2 contains 5 black and 5 white marbles. Find the probability that if a white marble was drawn, it came from Box 1.
c. suppose you have 100 marbles (50 back and 50 white) and are allowed to distribute them between the two boxes anyway you want. How should you do this so as to maximize the probability of that a black marble will be drawn?
If someone could help me out that would be great.
Thanks!

Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Use Bayes theorem for Conditional Probability. Cheers!
RELATED QUESTIONS
1. A committee of four people is to be chosen from a group of five women and six men.... (answered by stanbon)

can someone help me with these problems when you have a few min. thanks. Problem #1... (answered by stanbon)

1. Suppose that two cards are drawn without replacement from a standard deck of cards.... (answered by sudhanshu_kmr)

please help me. There are 6 black marbles, 6 white marbles, and 7 red marbles in a bag.... (answered by ikleyn)

A company that makes corn flex is putting prize coupons in some of the boxes to as a... (answered by ikleyn)

A company that makes corn flex is putting prize coupons in some of the boxes to as a... (answered by greenestamps)

Two boxes, A and B contain equal numbers of balls (black and white). A sample of 100... (answered by Boreal)

Two marbles are drawn without replacement from a jar with 4 black and 3 white marbles.... (answered by stanbon)

A bag contains four marbles: one red, one black, one white, and one orange. Two marbles... (answered by ewatrrr)