Re: If a is to be chosen at random from the integers between 1

Using the old school method

SET A : 1 , 2 , 3 , 4, 5

SET B : 6 , 7, 8, 9 ,10

Now for the numbers for be even ( a + b ) we can have either both numbers are even or both numbers are odd

Keeping SET B number constant 6 and varying A ( 1 , 2 ,3 ,4 ,5 )

1 + 6 => 7 ( Odd ) , 2 + 6 => 8 (Even) , 3 + 6 => 9 ( Odd ) , 4 + 6 => 10 (Even) , 5 + 6 => 11 ( Odd )

So using above probability of 2/5 will be even .

Keeping SET B number constant 7 and varying A ( 1 , 2 ,3 ,4 ,5 )

1 + 7 => 8 ( Even) , 2 + 7 => 9 (Odd) , 3 + 7 => 10 (Even) , 4 + 7 => 11 (Odd) , 5 + 7 => 12 ( Even)

So using above probability of 3/5 will be even for set B .

Hence P(A even , B even ) + P ( A odd , B odd ) = 3/5 * 2 /5 *2 = 12 / 25