# A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red?(ii) not red?

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Given:

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag.

To do:

We have to find the probability that the ball drawn is

(i) red.

(ii) not red

Solution:

(i) Number of red balls $=3$

Number of black balls $=5$

Total number of balls $=3+5=8$

This implies,

The total number of possible outcomes $n=8$.

Total number of favourable outcomes(drawing a red ball) $=3$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that the ball drawn is red $=\frac{3}{8}$

The probability that the ball drawn is red is $\frac{3}{8}$.

(ii) Number of red balls $=3$

Number of black balls $=5$

Total number of balls $=3+5=8$

This implies,

The total number of possible outcomes $n=8$.

Here, not a red ball implies that the ball drawn is black.

Total number of favourable outcomes(drawing a black ball) $=5$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that the ball drawn is not red $=\frac{5}{8}$

The probability that the ball drawn is not red is $\frac{5}{8}$.

Updated on 10-Oct-2022 13:25:43