Question
Two dice are rolled once. Find the probability of getting such numbers on two dice whose product is a perfect square.
✓
Answer
If two dice are rolled together, the possible oucomes are:
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)
$=\frac{8}{36}$
$=\frac{2}{9}$
(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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