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A bag contains 3 red, 5 black and 7 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is either red or white.

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715

15

815

23

answer is D.

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Detailed Solution

Given that a bag contains 3 red, 5 black and 7 white balls.
We need to find the probability that if a ball is drawn at random, it is either a red or a white ball.
Probability of an event E is defined as:

P (E) = \frac{Number of favorable outcomes}{Total number of possible outcomes}

There are 3 red, 7 white and 5 black balls in a bag, therefore, total number of balls are

3 + 7 + 5 = 15

Hence, the total number of possible outcomes is 15.
There are 3 red balls and 7 white balls, therefore, the number of favorable outcomes will be:

3 + 7 = 10

Let

R W

be the event that a ball drawn is either red or white.
Now, the probability of drawing either a red or a white ball is:

P (RW) = \frac{10}{15}

\Rightarrow P (RW) = \frac{2}{3}

The probability of drawing either a red or a white ball is

23

.
Therefore, option 4 is correct.

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