If you roll a die what is the probability you will roll aa 6

If you roll a die what is the probability you will roll

a-a 6

b- an even number

c-a number divisible by 3

d-if you roll a pair of dice what is the probablity that you will roll 2 6s

e-help-an even number on one and an odd number on the other

f-help-matching numbers

g-two numbers over four

...seems simple enough but i got e and f wrong according to my book...what makes them different and why

a) probability to roll a six = 1/6

b) probability to roll an even number = 3/6 = 1/2 (Since there are 3 even numbers out of 6)

c) probability to roll a number divisible by 3 = 2/6 = 1/3 (Since there are 2 numbers out of 6 that are divisible by 3 :- 3 and 6)

d) probablity that you will roll 2 6s = 1/6 * 1/6 = 1/36

e) probablity that you will roll an even number on one and an odd number on the other

= 3/6 * 3/6 * 2 = 1/2

There are 3 even and odd numbers in each case out of 6

2 is multiplied since one can get even number on the first die or the second die and similarly for odd numbers

f) probablity that you will roll matching numbers = 1 * 1/6 = 1/6

Let you get any number on the first die - hence probability is 1

For getting the same number: - probability is just 1/6 on th esecond die

g) probablity that you will roll two numbers over four = 2/6 * 2/6 = 1/9 {since there are 2 numbers over 4 :- 5 and 6}