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

2.78%

Explanation:

Probability Formula

`\sf Probability\:of\:an\:event\:occurring = (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)=(1)/(6)`

The probability of rolling six is:

`\implies \sf P(x = 6)=(1)/(6)`

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

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