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in Probability by (50 points)
A dice is rolled twice and sum of numbers is observed.
(1) What is the probability that the number 4 has occurred on one of the dice, if the sum is 6?

(ii) What is the probability that the number 3 has occurred on one of the dice, if the sum is 4?

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1 Answer

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by (15.4k points)
When a die is rolled there are six possible outcomes.  If the die is rolled twice, there are thirty-six ( 6 x 6 = 36 ) possible outcomes.

(1) If the sum of the two rolls of the die is six, and the number 4 occurred on one of the rolls, then there were two possible ways that could have happened;  a four on the first roll and a two on the second roll, or a two on the first roll and then a four on the second roll. So the probability is 2/36 or 1/18.

(2) exactly similar to (1), there are two ways that this could happen so the probability again is 1/18.

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