Question

There is a box containing two white balls. One more ball was added (either white or...

There is a box containing two white balls. One more ball was added (either white or black, with equal probabilities). Then the balls inside the box were mixed, and one was taken out. It turned out to be white. Given this information, what is the probability that the next ball taken out will also be white?

Homework Answers

Answer #1

We are given here that:
P(3 white ) = P(2 white and 1 black) = 0.5

The probability that a white ball is drawn is computed using law of total probability here as:

= 1*0.5 + (2/3)*0.5

= 5/6

Given that the white ball is drawn, the probability that the next ball taken would also be white is computed here as:

We first compute the revised probabilities of having 3 white or 2 white, 1 black using Bayes theorem here as:
P(3 white ) = 0.5*1 / (5/6) = 0.6
P(2 white and 1 black) = 0.5*(2/3) / (5/6) = 0.4

Now the probability that the next ball that will be taken out will also be white is computed here as:

= 1*P(3 white) + (2/3)*(P(2 white and 1 black) )

= 1*0.6 + (2/3)*0.4

= 0.8667

Therefore 0.8667 is the required probability here.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Box A contains 5 white balls and 7 black balls. Randomly choose one ball. If it...
Box A contains 5 white balls and 7 black balls. Randomly choose one ball. If it is white ball, we randomly draw one more from box A, and if it is black, we choose one ball from box B, in which there are 7 white balls and 8 black balls. a) What is the probability that in the second draw we will choose a white ball? b) The second ball is white, what is the probability that the first one...
A box contains one white ball, two red balls, and three black balls. Make a box...
A box contains one white ball, two red balls, and three black balls. Make a box model. Five draws are made with replacement from the box. Find the chance that: a) A red ball is never drawn. b) A black ball appears exactly three times. c) A white ball appears at least once.
Two balls are drawn from a bag containing 5 white balls and 7 red balls. If...
Two balls are drawn from a bag containing 5 white balls and 7 red balls. If the first ball is replaced before the second is drawn, what is the probability that the following will occur? (Enter your probabilities as fractions.) (a) both balls are red (b) both balls are white (c) the first ball is red and the second is white (d) one of the balls is black
Two balls are drawn in succession out of a box containing 7 red and 3 white...
Two balls are drawn in succession out of a box containing 7 red and 3 white balls. Find the probability that the second ball was​ red, given that the first ball​ was: ​(A)  replaced before the second draw. ​(B)  not replaced before the second draw.
Two balls are drawn from a bag containing 4 white balls and 3 red balls. If...
Two balls are drawn from a bag containing 4 white balls and 3 red balls. If the first ball is replaced before the second is drawn, what is the probability that the following will occur? (Enter your probabilities as fractions.) (a) both balls are red (b) both balls are white (c) the first ball is red and the second is white (d) one of the balls is black A die is thrown twice. What is the probability that a 2...
From an urn containing 3 white and 2 black balls, two balls are drawn one after...
From an urn containing 3 white and 2 black balls, two balls are drawn one after the other without replacement. What is the probability that the first ball drawn is white and the second black?
Two balls are chosen at random from a closed box containing 9 white, 4 black and...
Two balls are chosen at random from a closed box containing 9 white, 4 black and 2 orange balls. If you win $2 for each black ball selected but lose $1 for each white ball selected, and letting X stand for the amount of money won or lost, what are the possible values of X and what are the probabilities associated with each X? What is the expected value of your winnings? (Note: round to the nearest dollar) A. Lose...
Suppose that there is a white urn containing three white balls and one red ball and...
Suppose that there is a white urn containing three white balls and one red ball and there is a red urn containing two white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red. -please state answer in fraction-
There are five red balls and three white balls in a box. An experiment consist of...
There are five red balls and three white balls in a box. An experiment consist of drawing three balls in succession. Once a ball is drawn, it is not replaced. a. What is the probability that two or more red balls will be obtained in the three draws? b. What is the probability that exactly two white balls and one red ball will be obtained in the three draws? c. Given a white ball is selected on the first draw,...
1. Two balls are drawn from a bag containing 9 white balls and 2 red balls....
1. Two balls are drawn from a bag containing 9 white balls and 2 red balls. If the first ball is replaced before the second is drawn, what is the probability that the following will occur? (Enter your probabilities as fractions.) (a) both balls are red (b) both balls are white (c) the first ball is red and the second is white (d) one of the balls is black 2.The table gives the results of a survey of 1000 people...