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Two dice are rolled together. Find the probability of getting such numbers on the two dice whose product is 12.
Two dice are rolled together. Find the probability of getting such numbers on the two dice whose product is 12.
Correct Answer – ` 2/9`
Number of all possible outcomes is 36.
Let E be the event of getting the product of numbers on the two dice, as a perfect square.
Then, the favourable outcomes are
(1,1),(1,4),(4,1),(2,2),(3,3),(4,4),(5,5),(6,6).
Number of favourable outcomes = 8.
` :. P(E ) = 8/ 36 = 2/9`.
Number of all possible outcomes = 36
Let E be the event of getting all those numbers whose product is 12.
These number are (2,6),(3,4),(4,3) and (6,2)
Therefore, p(getting all those numbers whose product is 12) = P(E) = \(\frac{number\,of\,outcomes\,favorable\,to\,E}{number\,of\,all\,possible\,outcomes}\) = \(\frac{4}{36}\) = \(\frac{1}{9}\)
Thus, the probability of getting all those numbers whose product is 12 is \(\frac{1}{9}\).