A number 'a' is selected at random from the numbers 1,4,9,16 and another number 'b' is selected from the numbers 1, 2, 3, 4. Find the probability . . .

Question : A number 'a' is selected at random from the numbers 1,4,9,16 and another number 'b' is selected from the numbers 1, 2, 3, 4. Find the probability that the (i) product of a and b is more than 10 (ii) value of a+b is more than 15.

Doubt by Muskan

Solution : 

Total possible outcomes =
{(1,1), (1,2), (1,3), (1,4),
(4,1), (4,2), (4,3), (4,4), 
(9,1), (9,2), (9,3), (9,4), 
(16,1), (16,2), (16,3), (16,4)}=16

i) Product of 'a' and 'b' is more than 10 =
{(4,3), (4,4),(9,2), (9,3), (9,4), 

(16,1), (16,2), (16,3), (16,4)}= 9

P(Product of 'a' and 'b' is more than 10) = 9/16

ii) Value of a+b is more than 15 = 
{(16,1), (16,2), (16,3), (16,4)}=4

P(Value of a+b is more than 15) = 4/16 = 1/4