Question

An urn contains 3 red and 5 black balls a ball is drawn at random two balls are selcted at random with replacemnt

Answer 1

Step-by-step explanation:

An urn contains 3 red and 5 black balls. A ball is drawn at random, its colour is noted and returned to the urn. Moreover, 2 additional balls of the colour noted down, are put in the urn and then two balls are drawn at random (without replacement) from the urn.

Answer 2

Given:

A Urn contains 3 red and 5 black balls .

2 balls are drawn at random with replacement.

To Find:

1) probability that both are red balls.

2) probability that both are black balls

3) probability that 1 is red and 1 is black ball.

Solution:

When a ball is picked at random.

Probability that the ball is of a specific color is equal to the ratio of favorable outcomes and total outcomes.

Since two balls are drawn one by one with replacement

1)Probability that both the balls drawn at random are red balls.

$P(R) = (\frac{3}{8})(\frac{3}{8}) = \frac{9}{64}$

2) Probability that both balls drawn are black

$P(B) = (\frac{5}{8})(\frac{5}{8}) = \frac{25}{64}$

3) Probability that one ball is red and other ball is black

 $P(R+B) = (\frac{3}{8})(\frac{5}{8}) = \frac{15}{64}$

Required probabilities are 1) $\frac{9}{64}$2) $\frac{25}{64}$ 3) $\frac{15}{64}$