In a single toss of a fair die, what are the odds against the event that number 3 or 4 turns up? - Mathematics and Statistics

Sum

In a single toss of a fair die, what are the odds against the event that number 3 or 4 turns up?

Solution

When a fair die is tossed once, the sample space S is given by

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

∴ n(S) = 6

Let A ≡ the event that number 3 or 4 turns up

∴ A = {3, 4}

∴ n(A) = 2

∴ P(A) = ("n"("A"))/("n"("S")) = 2/6 = 1/3

∴ P(A') = 1 – P(A) = 2/3

∴ odds against event A = P(A') : P(A)

= 2/3 : 1/3

= 2 : 1

Concept: Odds (Ratio of Two Complementary Probabilities)
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