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:

$P(rolling\text{ a 3\rparen = }\frac{1}{6}$

The probability of rolling a 5:

$P(rolling\text{ a 5\rparen = }\frac{1}{6}$

The probability of rolling 3 thrice and 5 once is:

$\begin{gathered} =\text{ P\lparen3\rparen }\times\text{ P\lparen3\rparen }\times\text{ P\lparen5\rparen} \\ =\text{ }\frac{1}{6}\text{ }\times\text{ }\frac{1}{6}\text{ }\times\text{ }\frac{1}{6} \\ =\text{ }\frac{1}{216} \end{gathered}$

Answer:

$\frac{1}{216}$