Question

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?

Class X1 - Maths -Probability Page 408

Answer 1

Total number of ways for selecting 5 marbles out of 60 marbles n(S) = ⁶⁰C₅

(i) all will be blue .
Let E is the event all marbles will be blue then,
n( E ) = 5 marbles out of 20 marbles = ²⁰C₅
so, P( E ) = n(E)/n(S)
= ²⁰C₅ / ⁶⁰C₅

(ii) at least one will be green .
use formula ,
P(E') = 1 - P(E')
e.g P(at least one green ) = 1 - P(no green )
but P( no green ) = P(red + blue ) = ³⁰C₅ / ⁶⁰C₅
so, P( at least one green ) = 1 - P(red + blue )
= 1 - ³⁰C₅ / ⁶⁰C₅