Two dice are rolled once. Find the probability of getting such nu… - Vidyadip

Question

Two dice are rolled once. Find the probability of getting such numbers on two dice whose product is a perfect square.

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Answer

If two dice are rolled together, the possible oucomes are:

$(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)$

$(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)$

$(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)$

$(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)$

$(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)$

$(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)$

So, there are $36$ outcomes.
The be a following outcomes will give the product to be a perfect square.
$(1, 1), (1, 4), (2, 2), (3, 3), (4, 1), (4, 4), (5, 5), (6, 6)$
So, there are $8$ possible outcomes.
p(getting number whose product is a perfect square)
$=\frac{8}{36}$
$=\frac{2}{9}$

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