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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?Can I have an easy explaination for how and why we use combination to do this

Shivankit , 7 Years ago
Grade 11
anser 1 Answers
Arun

Last Activity: 7 Years ago

Dear student
 
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
 
 
Regards
Arun (askIITians forum expert)

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