Let A and B be two events such that their probabilities P(A) and P(B) are the roots of the quadratic equation 12x^2 - 7x + 1 = 0 . If the probability of occurrence of at least one of these events is 5 12 , then the value of P(A'|B') + P(B'|

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Let A and B be two events such that their probabilities P(A) and P(B) are the roots of the quadratic equation 12x^2 - 7x + 1 = 0 . If the probability of occurrence of at least one of these events is 5 12 , then the value of P(A'|B') + P(B'|A') is equal to

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Correct answer: C. 119 72

First, find the roots of the given quadratic equation: 12x^2 - 7x + 1 = 0 12x^2 - 4x - 3x + 1 = 0 4x(3x - 1) - 1(3x - 1) = 0 (4x - 1)(3x - 1) = 0 The roots are x = 1 3 and x = 1 4 . Let P(A) = 1 3 and P(B) = 1 4 . Given that P(A B) = 5 12 . By De Morgan's laws, the probability of neither event occurring is: P(A' B') = 1 - P(A B) = 1 - 5 12 = 7 12 The probabilities of the complementary events are: P(A') = 1 - P(A) = 1 - 1 3 = 2 3 P(B') = 1 - P(B) = 1 - 1 4 = 3 4 Now, calculate the required conditional probabilities:

Let A and B be two events such that their probabilities P(A) and P(B) are the roots of the quadratic equation 12x^2 - 7x + 1 = 0 . If the probability of occurrence of at least one of these events is 5 12 , then the value of P(A'|B') + P(B'|A') is equal to

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