Two different dice are thrown simultaneously. Find the probability of getting :
(i) a number greater than 3 on each dice
(ii) an odd number on both dice.

Question

Two different dice are thrown simultaneously. Find the probability of getting : (i) a number greater than 3 on each dice (ii) an odd number on both dice.

KnowledgeBoat · Accepted Answer

When two different dice are rolled together, the total number of outcomes is 6 × 6 i.e. 36 and all outcomes are equally likely. The sample space of the random experiment has 36 equally likely outcomes. The sample of the experiment S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).} It consists of 36 equally likely outcomes. (i) Let A be the event of getting 'a number greater than 3 on each dice', then A = {(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}. ∴ The number of outcomes favourable to event A = 9. ∴ P(a number greater than 3 on each dice) = Hence, the probability of getting a number greater than 3 on each dice is . (ii) Let B be the event of getting 'an odd number on both dice', then A = {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)}. ∴ The number of outcomes favourable to event B = 9. ∴ P(an odd number on both the dice) = Hence, the probability of getting an odd number on both the dice is .

Mathematics

Two different dice are thrown simultaneously. Find the probability of getting :
(i) a number greater than 3 on each dice
(ii) an odd number on both dice.

Probability

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