Question

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?

Answer 1

Total number of marbles = 10 + 20 + 30 = 60
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.
∴ Probability that all marbles will be blue =²⁰C_{5 / ⁶⁰}C₅

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

∴ Probability that no marble is green = 30C5 / 60C5
Probability that at least one marble is green = 1 – (30C5 / 60C5)