Question

Using the slot method and multiple cases, calculate the probability that you would roll 3 sixes with four standard dice.

Answer 1

Answer:

$Pr = \frac{1}{216}$

Step-by-step explanation:

 The sample space of a single dice is:

$S = \{1,2,3,4,5,6\}$

$n(S) = 6$

Required:

The probability of rolling 3 sixes

In a sample space of a roll of die, we have:

$n(6) = 1$

In a roll of dice, the probability of rolling a 6 is:

$P(6) = \frac{n(6)}{n(S)}$

$P(6) = \frac{1}{6}$

In 3 rolls, the probability is:

$Pr = P(6)^3$

$Pr = [\frac{1}{6}]^3$

$Pr = \frac{1}{216}$