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If A and B are two independent events such that P(A)=47P(A) = \frac{4}{7} and P(B)=27P(B) = \frac{2}{7} then P(A‾∩B‾)P(\overline{A} \cap \overline{B}) equals

Solution

✅ Correct Option: 4

If AA and BB are independent, so are their complements.

P(A‾)=1−47=37P(\overline A)=1-\frac47=\frac37 and P(B‾)=1−27=57P(\overline B)=1-\frac27=\frac57.

Hence P(A‾∩B‾)=37×57=1549P(\overline A\cap\overline B)=\frac37\times\frac57=\frac{15}{49}.

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