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Mathematics

A die is thrown once. What is the probability that the

(i) number is even

(ii) number is greater than 2?

Probability

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Answer

(i) Dice is thrown once
    Sample space = {1, 2, 3, 4, 5, 6} which has 6 likely outcomes.

Let E1 be the event of getting a even number, then number of favourable outcomes to E1 = 3

P(E1)=No. of favourable outcomes to E1Total no. of possible outcomes=36=12.P(E1) = \dfrac{\text{No. of favourable outcomes to } E1}{\text{Total no. of possible outcomes}} = \dfrac{3}{6} = \dfrac{1}{2}.

Hence, the probability of getting a even no. is 12\dfrac{1}{2}.

(ii) Let E2 be the event of getting a number greater than 2, then number of favourable outcomes to E2 = 4

P(E2)=No. of favourable outcomes to E2Total no. of possible outcomes=46=23.P(E2) = \dfrac{\text{No. of favourable outcomes to } E2}{\text{Total no. of possible outcomes}} = \dfrac{4}{6} = \dfrac{2}{3}.

Hence, the probability of getting a no. greater than 2 is 23\dfrac{2}{3}.

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