What is the probability of rolling a dice twice and getting a six?

2 answers:

kondor19780726 [428]3 years ago

5 0

1/6 if you are looking for it in fraction form. Because there are 6 side on a dice, and every one of them count as one sixth of the dice. So 1/6 would be your final answer.

Mekhanik [1.2K]3 years ago

3 0

$\huge \boxed{ \fcolorbox{black}{aqua}{Answer}}$

There are a total of 6 x 6 = 36 possible outcomes when a fair die is rolled twice. Of the 36 possible outcomes, there are 6 doubles: 1-1, 2-2, 3-3, 4-4, 5-5, and 6-6. Thus, the probability of getting a double is 6/36 = 1/6.

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3 years ago

likoan [24]

It's easy to show that $7\tan(4x)$ is strictly increasing on $x\in\left[0,\frac\pi8\right]$ . This means

$M = \max \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/12} = 7\sqrt3$

and

$m = \min \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/16} = 7$

Then the integral is bounded by

$\displaystyle 7\left(\frac\pi{12} - \frac\pi{16}\right) \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le 7\sqrt3 \left(\frac\pi{12} - \frac\pi{16}\right)$