Question

two different integers are randomly chosen from the set$$\{ -5, -8, 7, 4, -2 \}.$$what is the probability that their product is negative? express your answer as a common fraction.

Answer 1

The probability that the product of two different integers chosen from the set is negative is 3/5.

Step-by-step explanation:

To find the probability that the product of two different integers chosen from the given set is negative, we need to determine the total number of possible outcomes and the number of outcomes where the product is negative.

The total number of possible outcomes is C(5, 2) = 10, where C(n, r) represents the number of combinations of n items taken r at a time.

Now, let's count the number of outcomes where the product is negative. There are 3 negative numbers (−5, −8, −2) and 2 positive numbers (7, 4) in the set.

The number of outcomes where the product is negative is C(3, 1) * C(2, 1) = 6.

Therefore, the probability that the product of two different integers chosen from the set is negative is 6/10 = 3/5.