Question

A box contains 4 red balls, 5 green balls and 6 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?
 $
  {\text{A}}{\text{. }}\dfrac{2}{5} \\
  {\text{B}}{\text{. }}\dfrac{3}{5} \\
  {\text{C}}{\text{. }}\dfrac{1}{5} \\
  {\text{D}}{\text{. }}\dfrac{7}{{15}} \\
  $

Answer 1

Hint: Here, we go through by finding the favorable outcome that means the number of outcomes of green balls or red balls and finding the total number of outcomes that is the total number of all balls. Then use the formula to find the probability,
 $ {\text{ = }}\dfrac{{{\text{favorable outcome of red}}}}{{{\text{total number of outcome}}}} + \dfrac{{{\text{favorable outcome of green}}}}{{{\text{total number of outcome}}}} $

Complete step-by-step answer:
First of all we have to calculate total number of ball in a bag $ {\text{ = 6W + 4R + 5G = 15}} $ balls
Here $ {\text{W = }} $ white balls, $ {\text{R = }} $ red balls and $ {\text{G = }} $ green balls
This is the total no of outcome when one ball is drawn $ {\text{ = 15}} $ outcomes
Favorable outcome of green ball $ {\text{ = }} $ there are 5 green balls $ {\text{ = 5}} $
 $ \therefore P({\text{getting a green ball) = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total outcome}}}} = \dfrac{5}{{15}} $
Favorable outcome of red ball $ {\text{ = }} $ there are 4 red balls $ {\text{ = 4}} $
 $ \therefore P({\text{getting a red ball) = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total outcome}}}} = \dfrac{4}{{15}} $
 $ \therefore $ P (getting either red or green balls) = P (getting red) + P (getting green)
 $ {\text{ = }}\dfrac{{{\text{favorable outcome of red}}}}{{{\text{total number of outcome}}}} + \dfrac{{{\text{favorable outcome of green}}}}{{{\text{total number of outcome}}}} $
 $ {\text{ = }}\dfrac{4}{{15}} + \dfrac{5}{{15}} = \dfrac{9}{{15}} = \dfrac{3}{5} $
Hence option B is the correct answer.

Note: - Whenever we face such a type of question the key concept for solving the question is first you have to find the probability of drawing single balls and for finding the probability of either red or green we have to add the probability of the single balls.