A bag contains 6 red, 5 black and 4 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is red or white.

# A bag contains 6 red, 5 black and 4 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is red or white.

1. A
$\frac{7}{3}$
2. B
$\frac{2}{3}$
3. C
$\frac{5}{3}$
4. D
$\frac{1}{3}$

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### Solution:

Given that there are 6 red, 4 white and 5 black balls in a bag.
We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total possible outcomes n}\left(S\right)}$
Total number of balls are:
$6+4+5=15$
$⇒n\left(S\right)=15$
Let E be the event of getting red or white balls.
Total number of red or white balls is:
$6+4=10$
$⇒n\left(E\right)=10$
The probability of getting red or white ball is,
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total number of outcomes n}\left(S\right)}$
$⇒P\left(E\right)=\frac{10}{15}$
$⇒P\left(E\right)=\frac{2}{3}$ Thus, the probability of getting red or white ball is $\frac{2}{3}$.
Hence, option 2 is correct.

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