Question

You roll a fair die. What are the odds against landing on factors of 3?

Answer 1

Given that, we toss a fair die once.

Then the sample space, S will be

S = { 1,2,3,4,5,6 }

Let us define an event E such that

E : A factor of 3 is landed up

Then the outcomes favourable to E are

{ 1,3 }

Then

P(E)= n(E) / n(S) = 2/6 = 1/3

Hence, P(E) = 1/3

And P(E')= 1 - P(E) = 1 - 1/3 = 2/3

Then the odds in favour of landing a factor of 3 are

P(E) / (1- P(E) ) = (1/3)/(2/3) = (1/2) = 1:2

Similarly, odds against landing a factor of 3 are

( 1-P(E) ) / P(E) = (2/3) / (1/3) = ( 2/1 ) = 2:1

This answers your question.

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