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A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random.

What is the probability that the marble taken out will be not green.

Answer:

**Solution:**

When one event happens if and only if the other one doesn't, two occurrences are said to be complimentary. The probability of two complementary events add up to one.

Given,

A box containing 5 red, 8 white and 4 green marbles.

So, the total no. of possible outcomes = 17 (5 red + 8 white + 4 green)

Let E= event of getting a green marble

Number of favourable outcomes = 4 (as 4 green marbles)

Probability, P(E) = Number of favourable outcomes/ Total number of outcomes

P(E) = 4/17

So,

\overline{\mathrm{E}}=\text { Event of getting not a green marble }

Then we know that,

\begin{aligned} &P(\bar{E})=1-P(E) \\ &P(\bar{E})=1-\frac{4}{17} \\ &P(\bar{E})=\frac{13}{17} \end{aligned}

**Therefore, the probability that the marble taken out is not green is 13/17.**

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