Question

In: Statistics and Probability

There are 2 boxes. The first box contains 2 white and 5 black balls. The second...

There are 2 boxes. The first box contains 2 white and 5 black balls. The second box contains 4 white and 7 black balls. A random box is chosen and from it a random ball is drawn. a) What is the probability that the ball is white? b) If the ball is known to be white, what is the probability that it came from the 1st box?

Solutions

Expert Solution

There are 2 boxes.

The first box contains 2 white and 5 black balls.

The second box contains 4 white and 7 black balls.

A random box is chosen; from it a random ball is drawn.

Question (a)

We have to find the probability that the ball is white.

Let,

B1=Event that Box 1 is drawn.

B2=Event that Box 2 is drawn.

W=Event that white ball is drawn.

B=Event that Black ball is drawn.

It is given that

Now, we have to find

By total probability theorem, this becomes

So, the probability that the ball is white is 20/77.

Question (b)

We have to find the probability that the ball came from the first box, given that the ball is white.

So, basically we have to find

By using Bayes' theorem, it becomes

So, the probability that the first ball came from box 1, given that it is known to be white, is 11/20.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose 2 boxes: - Box #1 contains: + 5 Black balls. + 6 White balls. -...

Suppose 2 boxes: - Box #1 contains: + 5 Black balls. + 6 White balls. - Box #2 contains: + 8 Black balls. + 4 White balls. - Two balls are drawn from Box #2 and placed into Box #1. - A ball is drawn from Box #1. 1- What is the probability that the ball drawn from Box #1 is White? 2- Suppose that the ball drawn from Box #1 is White, then what is the probability that at...

Suppose 2 boxes: - Box #1 contains: + 5 Black balls. + 6 White balls. -...

Following are three boxes containing balls. Box #1 contains 2 black balls and 1 white ball....

Following are three boxes containing balls. Box #1 contains 2 black balls and 1 white ball. Box #2 contains 2 black balls and 2 white balls. Box #3 contains 1 black ball and 2 white ball. Draw a ball from Box 1 and place it in Box 2. Then draw a ball from Box 2 and place it in Box 3. Finally draw a ball from Box 3 . What is the possibility that the last ball drawn, from Box...

Problem 1 A box A contains 5 white and 4 black balls; another box B contains...

Problem 1 A box A contains 5 white and 4 black balls; another box B contains 3 white balls and 5 black ones. 3 balls are transferred from box A to box B and one ball is taken from box B. What is the probability that it is white?

Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box 2 contains...

Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box 2 contains 5 red balls, 3 green balls and 1 white ball. One ball of unknown color is transferred from Box 1 to Box 2. (a) What is the probability that a ball drawn at random from Box 2 is green? (b) What is the probability that a ball drawn from Box 1 is not white?

Two boxes are labelled I and II. Box I contains 4 black balls and 6 white...

Two boxes are labelled I and II. Box I contains 4 black balls and 6 white balls. Box II contains 2 black balls and 8 white balls. A player randomly selects one box and then randomly draws 2 balls without replacement from the selected box. 1) What is the probability of obtaining 2 black balls? 2) Given that 2 black balls are obtained, what is the probability that Box I is selected? 3) Suppose that 20 players conduct the game...

A box contains three white balls, two black balls, and one red ball. Three balls are...

A box contains three white balls, two black balls, and one red ball. Three balls are drawn at random without replacement. Let Y1 be the number of white balls drawn, and Y2 the number of black balls drawn. Find the distribution of Z = Y1 × Y2

There are 2 white balls, 9 black balls and 29 green balls in a box. We...

There are 2 white balls, 9 black balls and 29 green balls in a box. We draw a ball twice, without replacement. Let X and Y denote the number of white and black balls, respectively, among the drawn. Calculate Cov(X,Y).

Urn A contains four white balls and three black balls. Urn B contains six white balls...

Urn A contains four white balls and three black balls. Urn B contains six white balls and seven black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was white given that the second ball drawn was white? (Round your answer to three decimal places.) I can't seem to figure this out! Please help! Thank you!

An urn contains 11 white balls and 5 black balls. A simple random sample with replacement...

An urn contains 11 white balls and 5 black balls. A simple random sample with replacement (wr) of size: n = 2 is drawn from the urn. Calculate the probability that the sample contains one ball of each color. at least four decimal places.

Subjects