When two unbiased dice are tossed simultaneously, the
numbers that appear on the top surface of the two dice are a
and b.What is the probability that a^b is a perfect square?
(a^b=a to the power of b)
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Answer Posted / sriram
if the a^b is a perfect square means a to the power of b so
possibilities are
1^2 = 1 = 1^1 = 1^3 = 1^4 = 1^5 = 1^6
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
n(S) = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),...
(3,1),(3,3),...
...
...
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)} = 36
n(E) = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,2),(3,2),(4,2),(5,2),(6,2)} = 11
p(a^b is a perfect square) = n(E) / n(S)
= 11 / 36
| Is This Answer Correct ? | 3 Yes | 5 No |
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