Question

A bag contains 7red, 2blue and 4 green balls. What is the probability of getting a ball that is neither red nor blue?
A: \[11/13\;\;\]
 B: \[2/13\;\]
 C: \[1/2\]
 D: \[2/7\]

Answer 1

Hint: Here we will use the formula of probability. We will look at the number of favorable outcomes and the total number of outcomes. Probability is nothing but the ratio of number of favorable outcomes to the total number of outcomes.

Complete step-by-step answer:
In this question we have to find the probability of getting neither red nor blue that means we have to find the probability of getting balls other than red and blue i.e. green balls
We know that probability of any event is
\[\Rightarrow P\left( e \right) = \dfrac{{Number{\text{ }}of{\text{ }}favorable{\text{ }}outcomes}}{{Total{\text{ }}number{\text{ }}of{\text{ }}outcomes}}\]
Here favorable event is getting green balls
Number of green balls \[ = 4\]
Total number of balls $ = Number{\text{ }}of{\text{ }}red{\text{ }}balls + Number{\text{ }}of{\text{ }}green{\text{ }}balls + Number{\text{ }}of{\text{ }}blue{\text{ }}balls $
So, Probability of getting green balls
\[
   = {\text{ }}P{\text{ }}\left( {getting{\text{ }}green{\text{ }}balls} \right){\text{ }} \\
   = {\text{ }}\dfrac{{Number{\text{ }}of\;green{\text{ }}balls}}{{Total{\text{ }}no.{\text{ }}of{\text{ }}balls}}\; \\
\]
 $\Rightarrow P{\text{ }}\left( {getting{\text{ }}green{\text{ }}balls} \right){\text{ }} = {\text{ }}4/13 $

Note: In such a problem we start with looking at the favorable outcome then count of the favorable outcome. Then we look at the total number of outcomes. In different questions favorable outcomes can be different according to the condition in the question.