Question

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

a. 3 even and 1 odd numbers
b. 2 even and 2 odd numbers

Answer 1

a)0.25

b)0.375

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 =
`(3)/(6)=(1)/(2)`

Probability of getting odd =
`(3)/(6)=(1)/(2)`

4 dices are rolled together

a)P(3 even and 1 odd numbers)

P(3 even and 1 odd numbers)=
`^4C_3 ((1)/(2))^3 ((1)/(2))^1`

P(3 even and 1 odd numbers)=
`(4!)/(3!1!) ((1)/(2))^3 ((1)/(2))^1 =0.25`

b)P(2 even and 2 odd numbers)

P(2 even and 2 odd numbers)=
`^4C_2 ((1)/(2))^2 ((1)/(2))^2`

P(3 even and 1 odd numbers)=
`(4!)/(2!2!) ((1)/(2))^2 ((1)/(2))^2`=0.375