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2 years ago

If you roll two fair six-sided dice what is the probability that the sum is:

Mathematics

1 answer:

blsea [12.9K]2 years ago

6 0

Answer: If you roll two fair six-sided dice, the probability that the sum is 5 or lower is 5/18.

Explanation: Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

For an experiment having n number of outcomes, the number of favorable outcomes can be denoted by x

Let ‘x’ be the number on the first dice.

‘Y’ be the number on second dice.

We have to find the probability that the sum is 5 or lower i.e. (x + y) <= 5.

Total number of possible results from two six-sided dice is 6 × 6 = 36.

The possible results that the sum is lower than 4 is (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2) and (4,1).

Number of possible results for the sum is 5 or lower is 10.

The probability that the sum is 5 or lower = 10/36

=5/18

Therefore, the probability that the sum is 5 or lower is 5/18.

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Using the above formula, we have:

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The above shows that the side lengths of the square are congruent.

Next, calculate the slope of the sides using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m_{AB} = \frac{4 +2}{3 -2} = 6$

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Notice that the opposite slopes are congruent, and the adjacent slopes are opposite reciprocal.

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<h3>How to prove the shape is a right isosceles triangle</h3>

The legs of a right isosceles triangle are congruent, and the legs are perpendicular.

So, we start by calculating the lengths of the legs using the following distance formula

$d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}$

Using the above formula, we have:

$XY = \sqrt{(5-4)^2 + (-1-4)^2} = \sqrt{26$

$XZ = \sqrt{(5-0)^2 + (-1+2)^2} = \sqrt{26$

The above shows that the legs of the right isosceles triangle are congruent.

Next, calculate the slope of the legs using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m_{XY} = \frac{5-4}{-1 -4} = -\frac{1}{5}$

$m_{XZ} = \frac{5-0}{-1+2} = 5$

Notice that the slopes are opposite reciprocal.

The above highlight, and the equal legs show that the figure (2) is a right isosceles triangle

Read more about geometric shapes at:

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