# A dice has 6 faces. 2 faces are colored in blue, 3 faces are colored in red and 1 is green. The dice is rolled 4 times. What is the probability of the dice to show: a) blue, red, red, green (in this order); b) The same colors but in any order?

Feb 14, 2018

a) 1/24
b) 49/648

#### Explanation:

a) Since rolling dices are independent events, we combine probability by multiplying them.

$\frac{2}{6}$x$\frac{3}{6}$x$\frac{3}{6}$x$\frac{1}{2}$=$\frac{1}{24}$

b) There are 3 colors, hence the probability of rolling individual colors is just its probability to the power of 4.

${\left(\frac{2}{6}\right)}^{4}$+${\left(\frac{3}{6}\right)}^{4}$+${\left(\frac{1}{6}\right)}^{4}$= $\frac{49}{648}$