Question

A bag contains 4 red, 5 yellow and 6 pink balls. Two balls are drawn at random. What is the probability that none of the balls drawn are yellow in color?

Answer 1

0.3143

Explanation:

In probability:

AND = multiplication

OR = addition

There are 15 balls in total. However, when the first ball is drawn, it is NOT replaced

‘None of the balls drawn are yellow’ means we will be dealing with red and/or pink balls only.

One ball is RED AND other ball is PINK OR One ball is RED AND other ball is RED OR One ball is PINK AND other ball is PINK:

`= (4)/(15) .(6)/(14) +(4)/(15) .(3)/(14) + (6)/(15) .(5)/(14)`

`=(24)/(210)+(12)/(210) +(30)/(210)`

All the three fractions have the same denominator, therefore the resulting or simplified fraction will have the same denominator. In addition, everything written in the numerator level will be copied down as it is:

`=(24+12+30)/(210)`

`= (66)/(210)`

Divide both the numerator and denominator by the Highest Common Factor ‘6’:

`= (11)/(35)`

= 0.3143