Question

Two dice are rolled simultaneously find the probability of getting Earth some which is a multiple of 3

Answer 1

Answer:

probability of getting 3 multiple s is 4/12=1/3

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Answer 2

Appropriate Question :-

Two dice are thrown simultaneously. Find the probability of getting:

a multiple of 2 on one dice and a multiple of 3 on the other.

Solution :-

Elementary events associated to the random experiment of throwing two dice are :

• (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)

∴ Total number of elementary events = 6 × 6 = 36

Let A be the event of getting a multiple of 2 on one die and a multiple of 3 on the other. Then, the elementary events favourable to A are :

• (2, 3), (2, 6), (4,3), (4, 6), (6, 3), (6, 6), (3, 2), (3, 4), (3, 6), (6, 2), (6, 4)

∴ favourable number of elementary events = 11.

Hence,

$\dag \: \sf{Required \: Probability = \frac{11}{36}}$

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