What are the odds in favour for this event?
getting a perfect square when two number cubes labelled 1 to 6 are rolled and the numbers are multiplied.
i don't understand how to do this. please help. thank u :)
so its 12 to... but what would the unfavourable outcome be?? :S
No. If the first die has any number on it, the probability of the second die getting the same number is 1/6.
So the probability of getting a perfect square is 1/6
The unfavorable is 1-1/6
Note:
The favourable combinations are:
1,1 or 2,2 or 3,3 or 4,4 or 5,5 or 6,6 or 1,4 (becaue 1*4 is also a perfect square).
So they add up to 38/216=19/108
To determine the odds in favor of getting a perfect square when two number cubes labeled 1 to 6 are rolled and the numbers are multiplied, we need to first understand what a perfect square is.
A perfect square is a number that can be obtained by multiplying an integer by itself. For example, 1, 4, 9, 16, and 25 are all perfect squares because they are the result of multiplying a whole number by itself (1x1, 2x2, 3x3, 4x4, and 5x5, respectively).
Now, let's see what possible outcomes we can get by rolling two number cubes labeled 1 to 6 and multiplying the numbers:
Rolling a number cube can result in any number from 1 to 6. So the possible outcomes when rolling two number cubes would be:
1x1, 1x2, 1x3, 1x4, 1x5, 1x6
2x1, 2x2, 2x3, 2x4, 2x5, 2x6
3x1, 3x2, 3x3, 3x4, 3x5, 3x6
4x1, 4x2, 4x3, 4x4, 4x5, 4x6
5x1, 5x2, 5x3, 5x4, 5x5, 5x6
6x1, 6x2, 6x3, 6x4, 6x5, 6x6
Now, let's determine which of these outcomes are perfect squares. From the list above, we can see that the perfect squares are:
1x1 = 1
2x2 = 4
3x3 = 9
4x4 = 16
5x5 = 25
6x6 = 36
So, there are 6 possible outcomes that result in a perfect square.
Since there are a total of 36 possible outcomes (6 outcomes per roll, for two rolls), the odds in favor of getting a perfect square would be:
Odds in favor = Number of favorable outcomes / Number of possible outcomes
Odds in favor = 6 / 36
Simplifying the fraction, we get:
Odds in favor = 1 / 6
Therefore, the odds in favor of getting a perfect square when two number cubes labeled 1 to 6 are rolled and the numbers are multiplied are 1 to 6.
Both dice have to be the same to have a perfect square (1,1 or 2,2 or 3,3 or 4,4, or so on)
Think on that.
Figure the probability of getting two numbers the same on each die.