Question

During the Holi festival, Sonali filled 7 bottles with different coloured water – red, blue, green, pink, yellow, purple and orange. One bottle is selected at random. What is the probability of choosing the bottle with neither yellow nor pink?

Answer 1

Hint : This question is based on the probability. In this question there are a total of 7 different coloured water bottles given and out of these 7 bottles only one bottle is picked at random and we have to find the probability of the bottle being neither yellow nor pink.
The formula for the probability is given by-
${\rm{Probability = }}\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$

Complete step-by-step answer :
The colour of the water bottles - red, blue, green, pink, yellow, purple and orange.
So, the number of total possible outcomes $n = 7$
Now we have to pick a coloured bottle other than yellow and pink which means that we have 5 colours left - red, blue, green, purple, orange.
So, the number of favourable outcomes $n\left( E \right) = 5$
Now using the formula for the probability,
The probability of choosing neither yellow nor pink coloured bottle
$\Rightarrow P\left( E \right) = \dfrac{{n\left( E \right)}}{n}$
Substituting the values, we get,
$\Rightarrow P\left( E \right) = \dfrac{5}{7}$
Therefore, the probability of choosing neither yellow nor pink coloured bottle is $\dfrac{5}{7}$.

Note : The alternate method to solve this question is that we first find the probability of choosing either a yellow or pink coloured bottle. Which means that we have 2 favourable coloured bottles yellow and pink. Then by using the formula for the probability of an event we calculate the probability of choosing either a yellow or pink coloured bottle. Also, we know that the sum of the probabilities of an event occurring and not occurring is always 1. So, the probability of choosing neither yellow nor pink coloured bottle can be calculated by subtracting the value of the probability of choosing either yellow or pink coloured bottle with 1.