Probability

[hey_thr67]

If x is a randomly chosen integer between 1 and 20, inclusive, and y is a randomly chosen integer between 21 and 40, inclusive, what is the probability that xy is a multiple of 4?
(A) 1/4
(B) 1/3
(C) 3/8
(D) 7/16
(E) 1/2

[Anurag@Gurome]

If x is a randomly chosen integer between 1 and 20, inclusive, and y is a randomly chosen integer between 21 and 40, inclusive, what is the probability that xy is a multiple of 4?

Each group has 20 consecutive integers.
Hence, in each group there will be 20/2 = 10 even and 10 odd integers.
And, in each group there will be 20/4 = 5 multiples of 4.

There are three cases xy will NOT to be a multiple of 4:

• 1. both x and y are odd --> 10*10 = 100 pairs
  2. x is odd and y is even but not multiple of 4 --> 10*5 = 50 pairs
  3. y is odd and x is even but not multiple of 4 --> 10*5 = 50 pairs
  
  Hence, a total of (100 + 50 + 50) = 200 pairs

Total number of possible values of xy = 20*20 = 400

Hence, required probability = 1 - (200/400) = 1 - 1/2 = 1/2

The correct answer is E.