Question

Box I contains 7 red and 3 black balls; Box II contains 4 red and 5...

Box I contains 7 red and 3 black balls; Box II contains 4 red and 5 black balls. After a randomly selected ball is transferred from Box I to Box II, 2 balls are drawn from Box II without replacement. Given that the two balls are red, what is the probability a black ball was transferred?

Homework Answers

Answer #1

P(black ball transferred) = 3/10
P(Red ball transferred) = 7/10

When a ball is transferred from Box I to Box II there will be 10 balls in Box II and number of Red and Black will differ depending on the ball trasferred from Box I

required probability, P(black transferred | 2 Red) = P(2 Red | black transferred)*P(black transferred) / (P(2 Red | black transferred)*P(black transferred) + P(2 Red | red transferred)*P(red transferred))

P(2 Red | black transferred) = 4C2/10C2 = 0.1333
P(2 Red | red transferred) = 5C2/10C2 = 0.2222

P(black transferred | 2 Red) = 0.1333*0.3 / (0.1333*0.3 + 0.7*0.2222) = 0.2045

Ans: 0.2045

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
Exercise 2 A box contains 3 white balls, 4 red balls and 5 black balls. A...
Exercise 2 A box contains 3 white balls, 4 red balls and 5 black balls. A ball is picked, its color recorded and returned to the box(with replacement). Another ball is then selected and its color recorded. 1. Find the probability that 2 black balls are selected. 2. Find the probability that 2 balls of the same color are selected. Now 4 balls are picked with replacement 3.Find the probability no red balls are selected. 4.Find the probability that the...
A box contains 4 red and 6 black balls. Two balls are selected one after the...
A box contains 4 red and 6 black balls. Two balls are selected one after the other, a) What is the probability that the first ball selected is black and the second ball selected is also black, if the selection is done without replacement. b) What is the probability that the first ball selected is black and the second ball selected is red, if the selection is done without replacement. c) What is the probability that the first ball selected...
Box 1 contains 4 red balls, 5 green balls and 1 yellow ball. Box 2 contains...
Box 1 contains 4 red balls, 5 green balls and 1 yellow ball. Box 2 contains 3 red balls, 5 green balls and 2 yellow balls. Box 3 contains 2 red balls, 5 green balls and 3 yellow balls. Box 4 contains 1 red ball, 5 green balls and 4 yellow balls. Which of the following variables have a binomial distribution? (I) Randomly select three balls from Box 1 with replacement. X = number of red balls selected (II) Randomly...
Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 4 red balls...
Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 4 red balls and 1 black ball. Urn 3 contains 4 red balls and 3 black balls. If an urn is selected at random and a ball is drawn, find the probability that it will be red. enter your answer as a decimal rounded to 3 decimal places
In a box are 3 red balls and 5 blue balls. From this box are drawn...
In a box are 3 red balls and 5 blue balls. From this box are drawn 4 balls and placed in a second box. Given the ball drawn from the second box is red, what is the probability that 2 red and 2 blue balls were transferred from box 1 to box 2?
Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 1 red ball...
Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 1 red ball and 3 black balls. Urn 3 contains 3 red balls and 1 black ball. If an urn is selected at random and a ball is drawn, find the probability that it will be red. Enter your answer as a fraction in simplest form or a decimal rounded to 3 decimal places.
Urn 1 contains 4 red balls and 3 black balls. Urn 2 contains 1 red ball...
Urn 1 contains 4 red balls and 3 black balls. Urn 2 contains 1 red ball and 3 black balls. Urn 3 contains 4 red balls and 2 black balls. If an urn is selected at random and a ball is drawn, find the probability that it will be red. Enter your answer as a fraction in simplest form or a decimal rounded to 3 decimal places. P(red)=
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.
There are 8 black balls and 7 red balls in an urn. If 4 balls are...
There are 8 black balls and 7 red balls in an urn. If 4 balls are drawn without replacement, what is the probability that no more than 1 black ball is drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.
A bag contains 7 red balls and 5 white balls. Two balls are drawn without replacement....
A bag contains 7 red balls and 5 white balls. Two balls are drawn without replacement. (Enter your probabilities as fractions.) (a) What is the probability that the second ball is white, given that the first ball is red? (b) What is the probability that the second ball is red, given that the first ball is white? (c) Answer part (a) if the first ball is replaced before the second is drawn.