Question

A fair six sided die is rolled twice what is the probability it will end on one and then six

Answer 1

Total elements in sample space=6

P(1)

• 1/6

P(6)

• 1/6

P(1 and 6)

• (1/6)²
• 1/36
• 2.78%

Answer 2

Answer:

2.78%

Step-by-step explanation:

Probability Formula

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

We are told that the six-sided dice is fair. This means that each of the faces has the same probability of being rolled.

Therefore, the probability of rolling one is:

$\implies \sf P(x = 1)=\dfrac{1}{6}$

The probability of rolling six is:

$\implies \sf P(x = 6)=\dfrac{1}{6}$

Therefore, the probability of rolling one and then six is:

$\begin{aligned}\implies \sf P(x=1)\:and\:P(x=6) & = \sf \dfrac{1}{6} \times \dfrac{1}{6}\\& =\sf \dfrac{1}{36}\\& = \sf 0.0278\:(3\:s.f.)\\& = \sf 2.78\%\:(3\:s.f.)\end{aligned}$