Answer:
Therefore, the correct answer is 9/16.
Explanation:
To determine the probability that mn is an even integer, we need to consider the possible values of m and n.
Set P contains the elements (2, 3, 5, 5, 6), and set Q contains the elements (1, 2, 3, 4).
For mn to be an even integer, either m or n must be an even number.
In set P, there are two even numbers (2 and 6) out of a total of five elements. So, the probability of selecting an even number from set P is 2/5.
In set Q, there are two even numbers (2 and 4) out of a total of four elements. So, the probability of selecting an even number from set Q is 2/4 or 1/2.
To find the probability that mn is an even integer, we can consider the two cases:
If m is even and n is any number:
The probability of m being even from set P is 2/5, and the probability of n being any number from set Q is 1 (since any number can be selected from set Q). Therefore, the probability of mn being even in this case is (2/5) * 1 = 2/5.
If m is any number and n is even:
The probability of m being any number from set P is 1 (since any number can be selected from set P), and the probability of n being even from set Q is 1/2. Therefore, the probability of mn being even in this case is 1 * (1/2) = 1/2.
We can add these two probabilities to find the overall probability that mn is an even integer:
Probability = (2/5) + (1/2) = 4/10 + 5/10 = 9/10.
Therefore, the correct answer is 9/16.