Question

You roll a die three times. What is the probability ofrolling 3 twice and 5 once?

Answer 1

Given

The dice is rolled 3 times

The probability (P) of a dice can be calculated using the formula:

`P\text{ = }\frac{number\text{ of required outcomes}}{Total\text{ number of possible outcomes}}`

The probability of rolling a 3 is:

`P(rolling\text{ a 3\rparen = }(1)/(6)`

The probability of rolling a 5:

`P(rolling\text{ a 5\rparen = }(1)/(6)`

The probability of rolling 3 thrice and 5 once is:

`\begin{gathered} =\text{ P\lparen3\rparen }*\text{ P\lparen3\rparen }*\text{ P\lparen5\rparen} \\ =\text{ }(1)/(6)\text{ }*\text{ }(1)/(6)\text{ }*\text{ }(1)/(6) \\ =\text{ }(1)/(216) \end{gathered}`

Answer:

`(1)/(216)`