X = {- 4, - 2, 1, 3} Y = {- 1, 4, 5). If x is a number from set X, and y is a number from set Y, the probability that x + y is positive is closest to:

Question: X = {- 4, - 2, 1, 3} Y = {- 1, 4, 5). If x is a number from set X, and y is a number from set Y, the probability that x + y is positive is closest to:

Solution:
First, find the total number of possible outcomes by pairing each element of X with each element of Y.
Total outcomes = n(X) × n(Y) = 4 × 3 = 12.

Now, let's identify the pairs (x, y) where x + y > 0:
1. From x = - 4: (- 4, 5) → Sum = 1 [1 pair]
2. From x = - 2: (- 2, 4), (- 2, 5) → Sums = 2, 3 [2 pairs]
3. From x = 1: (1, 4), (1, 5) → Sums = 5, 6 [2 pairs] (Note: 1 + (- 1) = 0, which is not positive)
4. From x = 3: (3, - 1), (3, 4), (3, 5) → Sums = 2, 7, 8 [3 pairs]

Total favorable outcomes = 1 + 2 + 2 + 3 = 8.
Probability = Favorable outcomes/Total outcomes
∴ Probability = 8/12 = 2/3 ≈ 0.666...

Among the given options, 0.666... is closest to 0.7.
∴ The probability is closest to 0.7.