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 / aneesha
The combinations are the following:
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,2)(2,4)(2,6)
(3,2)(3,4)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,2)(5,4)(5,6)
(6,2)(6,4)(6,6)
Thus prob= 24/36 = 2/3 = 0.667
| Is This Answer Correct ? | 11 Yes | 4 No |
Answer / 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 |
Answer / gireesh puthumana
If A^B is a perfect square, then A must be equal to B. So the question in another words is what is the probability that A & B are equal.
Answer is:
All possible combinations when 2 dice are thrown are (1,1), (1,2)...(1,6),(2,1),(2,2)...(6,6) - 36
Desired combinations are (1,1),(2,3),(3,3),(4,4),(5,5),(6,6) - 6
So probability is : 6/36 = 1/6
| Is This Answer Correct ? | 18 Yes | 21 No |
Answer / dhanuja priya
if the no.s a and b are not be equal...then the answer will
be 20/36
the combinations are:
(1,2),(1,3),(1,4),(1,5),(1,6)
(2,4),(2,6)
(3,2),(3,4),(3,6)
(4,1),(4,2),(4,3),(4,5),(4,6)
(5,2),(5,4),(5,6)
(6,2),(6,4)
thus the ans will be=20/36=5/9
| Is This Answer Correct ? | 8 Yes | 20 No |
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