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Standard XII

Mathematics

Multinomial Theorem

Two fair dice...

Question

Two fair dice are rolled. Let A_i represents the event that the sum of the faces of the dice is
divisible by i. Then answer the following
Then for which one of the following pairs (i, J) the events A_i and A_J are independent

(4, 6)

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(3, 4)

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(2, 3)

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(2, 4)

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Solution

The correct option is C (2, 3)
$P (A_{2}) = \frac{18}{36} = \frac{1}{2} P (A_{3}) = \frac{1}{3}, P (A_{6}) = \frac{6}{36} = \frac{1}{6} = P (A_{2}) P (A_{3})$
$∴ A_{2} a n d A_{3}$ are independent

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Two fair dice are rolled. Let Ai represents the event that the sum of the faces of the dice is divisible by i. Then answer the following Then for which one of the following pairs (i, J) the events A­i and AJ are independent

The correct option is C (2, 3)P(A2)=1836=12P(A3)=13,P(A6)=636=16=P(A2)P(A3) ∴A2 and A3 are independent

Two fair dice are rolled. Let A_i represents the event that the sum of the faces of the dice is
divisible by i. Then answer the following
Then for which one of the following pairs (i, J) the events A_i and A_J are independent

The correct option is C (2, 3)
$P (A_{2}) = \frac{18}{36} = \frac{1}{2} P (A_{3}) = \frac{1}{3}, P (A_{6}) = \frac{6}{36} = \frac{1}{6} = P (A_{2}) P (A_{3})$
$∴ A_{2} a n d A_{3}$ are independent