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Mathematics Question on Probability

If A and B are two independent events such that P(A)>0,P(A) > 0, and P(B)≠1P(B)\ne 1, then P(A‾/B‾)P(\overline{A}/ \overline{B}) is equal to

A

1−P(A/B)1 - P(A / B)

B

1−P(A/B‾)1 - P(A / \overline{B})

C

1−P(A∪B)p(B)\frac{1-P(A \cup B)}{p(B)}

D

P(A‾)P(B‾)\frac{P(\overline{A})}{P(\overline{B})}

Answer

1−P(A/B‾)1 - P(A / \overline{B})

Explanation

Solution

Since,P(A/B‾)+P(A‾/B‾)P(A / \overline{B}) + P(\overline{A} / \overline{B})= 1
∴               P(A‾/B‾)=1−P(A/B‾)\therefore \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, P(\overline{A}/\overline{B})=1-P(A / \overline{B})