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Set P = (2, 3, 5, 5, 6) Set Q = (1, 2, 3, 4)

If m is randomly selected from Set P and n randomly selected from Set Q, what is the probability that mn is an even integer?


3/4

11/16

9/16

1/4

3/16​

1 Answer

3 votes

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.

User Radovix
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