Ashifur September 9, 2023 - 19:06
Problem: A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour?

View all: BASIC BANK LTD (CASHIR) WRITTEN QUESTION (MATH) SOLVE | 2018

Correct Answer: $\frac{41}{44}$

Explanation:

Given that. number of green ball = 5

so,Number of yellow ball = 4 and

so,Number of white ball = 3

so,Total ball=5+4+3= 12

so,Probability that the balls are same colour is

P(3 balls are same colours) = P(3 green) + P(3 yellow) + P (3 white)

= $\frac{5c_{3}}{12c_{3}}+\frac{4c_{3}}{12c_{3}}+\frac{3c_{3}}{12c_{3}}$

= $\frac{10}{220}+\frac{1}{220}+\frac{1}{220}$

= $\frac{10+4+1}{220}$ = $\frac{15}{220}$ = $\frac{3}{44}$

so, P (3 balls are same NOT colours) = 1-$\frac{3}{44}$ = $\frac{44-3}{44}$

= $\frac{41}{44}$

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