Question

You roll 4 fair, distinguishable, six-sided dice. What is the probability of rolling :______

Answer 1

Answer:

a)0.25

b)0.375

Step-by-step explanation:

Possible outcomes when dice are rolled : 1 ,2 ,3,4,5 ,6

Even= 2,4,6  

Odd = 1 ,3 , 5

Probability of getting even =$\frac{3}{6}=\frac{1}{2}$

Probability of getting odd = $\frac{3}{6}=\frac{1}{2}$

4 dices are rolled together

a)P(3 even and 1 odd numbers)

P(3 even and 1 odd numbers)=$^4C_3 (\frac{1}{2})^3 (\frac{1}{2})^1$

P(3 even and 1 odd numbers)=$\frac{4!}{3!1!} (\frac{1}{2})^3 (\frac{1}{2})^1 =0.25$

b)P(2 even and 2 odd numbers)

P(2 even and 2 odd numbers)=$^4C_2 (\frac{1}{2})^2 (\frac{1}{2})^2$

P(3 even and 1 odd numbers)=$\frac{4!}{2!2!} (\frac{1}{2})^2 (\frac{1}{2})^2$=0.375