A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that (i) all will be blue?  (ii) atleast one will be green?

Solution:

Total number of marbles = 10 + 20 + 30 = 60

The number of ways of drawing r different objects from n different objects is ⁿCᵣ.

Therefore, the number of ways of drawing 5 marbles from 60 marbles = ⁶⁰C₅

(i) All the drawn marbles will be blue if we draw 5 marbles out of 20 blue marbles.

5 blue marbles can be drawn from 20 blue marbles in ²⁰C₅ ways.

Therefore, the probability that all marbles will be blue ²⁰C₅/⁶⁰C₅

(ii) Number of ways in which the drawn marbles is not green ⁽²⁰ ⁺ ¹⁰⁾C₅ = ³⁰C₅

Hence, the probability that no marble is green = ³⁰C₅/⁶⁰C₅

Therefore,

The probability that at least one marble is green = 1 - ³⁰C₅/⁶⁰C₅

NCERT Solutions Class 11 Maths Chapter 16 Exercise ME Question 1

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that (i) all will be blue? (ii) atleast one will be green?

Summary:

The probability that (i) All marbles will be blue is ²⁰C₅/⁶⁰C₅ (ii) Atleast one marble will be green is 1 - ³⁰C₅/⁶⁰C₅