CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Axiomatic Approach

One urn conta...

Question

One urn contains two black balls (labelled $B_{1}$ and $B_{2}$ ). Suppose, the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then, a second ball is chosen at random from the same urn without replacing the first ball.

(i) Write the sample space showing all possible outcomes.

(ii) What is the probability that two black balls are chosen ?

(iii) What is the probability that two balls of opposite colour are chosen ?

Open in App

Solution

(i) ${| B_{1} B_{2}, | B_{1} W_{1}, | B_{2} B_{1}, | B_{2} W_{1}, | W_{1} B_{1} | W_{1} B_{2} | | W_{1} W_{2}, | | W_{1} B_{1}, | | W_{2} W_{1}, | | B_{1} W_{1}, | | B_{1} W_{2}}$

(ii) $\frac{1}{6}$

(iii) $\frac{2}{3}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The contents of three urns are as follows:
Urn 1 : 7 white, 3 black balls, Urn 2 : 4 white, 6 black balls, and Urn 3 : 2 white, 8 black balls. One of these urns is chosen at random with probabilities 0.20, 0.60 and 0.20 respectively. From the chosen urn two balls are drawn at random without replacement. If both these balls are white, what is the probability that these came from urn 3?

n

4

6

black balls. The

(n + 1) t h

5

5

black balls. Out of the

(n + 1)

urns is chosen an urn at random and two balls are drawn from it without replacement. Both the balls turn out to be black. If the probability that the

(n + 1) t h

urn was chosen to draw the ball is

\frac{1}{6}

, then the value of

n

Q. Suppose there are three urns containing 2 white and 3 black balls: 3 white and 2 black balls, and 4 white and one black ball respectively. There is equal probability of each urn being chosen. One ball is drawn from an urn chosen at random. The probability that a white ball is drawn is

\frac{k}{15}

. Find the value of

k

Q. There are two urns

U_{1}

U_{2}

U_{1}

2

8

black balls and

U_{2}

4

6

black balls. One urn is chosen at random and a ball is drawn and its colour noted and replaced. The process is repeated

3

times and as a result one ball of white colour and

2

of black are obtained. The probability that the urn chosen was

U_{1}

Q. An urn contains 5 red, 3 black and 2 white balls. If three balls are chosen at random then what is the probability that balls will be of different colours?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Axiomatic Approach

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Axiomatic Approach

Standard XI Mathematics

Join BYJU'S Learning Program

CrossIcon