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A die is thrown once, find the probability . . .

Question : A die is thrown once, find the probability of getting a number which is
a) a multiple of 2 or 3
b)  a multiple of 2 and 3.

Doubt by Nevaeh

Solution : 

Total number of possible outcomes when a dice is thrown once = {1,2,3,4,5,6} = 6

a) No. on the dice which is a multiple of 2  {2,4,6} = 3
No. on the dice which is a multiple of 3  {3,6} = 2

No. on the dice which is a multiple of 2 or 3 {2,3,4,6} = 4

P(
multiple of 2 or 3) = 4/6 = 2/3

b) No. on the dice which is a multiple of 2 and 3 {6} = 1

P(multiple of 2 and 3) = 1/6