State true or falseA box contains 7 red, 8 green and 5 white marbles. If one marble is drawn at random from the box, the probability that it is neither red nor white is 25.

# State true or falseA box contains 7 red, 8 green and 5 white marbles. If one marble is drawn at random from the box, the probability that it is neither red nor white is $\frac{2}{5}$.

1. A
True
2. B
False

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### Solution:

Given that there are 7 red, 5 white and 8 green marbles in a box.
Total number of marbles are,
$7+5+8=20$ $⇒n\left(S\right)=20$
Total number of green marbles, $n\left(E\right)=8$
We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total possible outcomes n}\left(S\right)}$
Probability of getting neither red nor white marble is equal to the probability of getting green marbles P(G) is,
$⇒P\left(G\right)=\frac{8}{20}$
$⇒P\left(G\right)=\frac{2}{5}$
Therefore, the probability of getting neither red nor white marble is $\frac{2}{5}$.
Hence, option 1 is correct and the statement is true.

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