probability

Question

Two intergers are chosen at random and multiplied. Find the probability that the product is even integer.

Comments

Lemme try.

Integers are chosen at random

P(even) =1/2

P(odd) =1/2

even x even =even // 1/2*1/2 =1/4

even x odd = even //  1/2*1/2 =1/4

odd x even = even //  1/2*1/2 =1/4

odd x odd = odd // 1/2*1/2 =1/4

Probability that product  is odd =1/4

Probability that product  is even= 1/4+1/4+1/4 =3/4

Correct me if I am wrong

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I think the same way : Three parallel cases :

1. Even*Even = Even

2. Even*Odd = Even

3. Odd*Even = Even

Probabiliy of selecting Even number = 1/2 = Probability of selecting Odd number before multiplying.

In each of the above three cases probabilty of getting a Even number after multiplying is 1/4

Net probabilty = 3*(1/4) = 3/4

Answer 1

Yes, it is $\frac{3}{4}$. Only odd multipled by odd gives odd product. All three cases yield even product.