Let there be two events A and B. with probabilities P(A)=x and P(B)=x−0.1 respectively. Knowing that they are independent and that their intersection has probability 0.0336, Determine the value of x.

The probability of the intersection of two independent events A and B is given by P(A and B) = P(A) * P(B). We are given that P(A and B) = 0.0336, P(A) = x, and P(B) = x - 0.1. Substituting these values into the formula, we get: 0.0336 = x * (x - 0.1) 0.0336 = x^2 - 0.1x x^2 - 0.1x - 0.0336 = 0 This is a quadratic equation that we can solve using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a where a = 1, b = -0.1, and c = -0.0336. Substituting these values into the formula, we get: x = (-(-0.1) ± sqrt((-0.1)^2 - 4(1)(-0.0336))) / 2(1) x = (0.1 ± sqrt(0.0101)) / 2 x = (0.1 ± 0.38) / 2 Solving for x, we get two possible values: x = 0.48 / 2 = 0.24 x = -0.28 / 2 = -0.14 Since probabilities cannot be negative, we can discard the second solution and conclude that x = 0.24. Therefore, the value of x is 0.24.