State true or false:A bag contains 6 red, 5 black and 4 white balls. A ball is drawn from the bag at random. The probability that white ball drawn is 415.

# State true or false:A bag contains 6 red, 5 black and 4 white balls. A ball is drawn from the bag at random. The probability that white ball drawn is $\frac{4}{15}$.

1. A
True
2. B
False

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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:
$⇒n\left(S\right)=15$
Let E be the event of getting a white ball.
Total number of white balls is 4.
$⇒n\left(E\right)=4$
The probability of getting a white ball is,
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total number of outcomes n}\left(S\right)}$
$⇒P\left(E\right)=\frac{4}{15}$
Thus, the probability of getting a white ball is $\frac{4}{15}$.
Therefore, the given statement is true.
Hence, option 1 is correct.

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