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  • Help me please, Let E and F be two independent events such that P(E) > P(F). The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2. Then

Let E and F be two independent events such that P(E) > P(F). The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2. Then

  • Option 1)

    P(E) = 1/3, P(F) = 1/4

  • Option 2)

    P(E) = 1/2, P(F) = 1/6

  • Option 3)

    P(E) = 1/2, P(F) = 1/6

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learned

 

Independent events -

If A and B are independent events then \overline{A} and \overline{B}  independent event.

- wherein

P\left ( \overline{A}\cap \overline{B} \right )= P\left ( \overline{A} \right )\cdot P\left ( \overline{B} \right )

 

 P(E\cap F)=P(E)P(F)=\frac{1}{12}\cdots (1)

P(E^{c}\cap F^{c})=P(E^{c})P(F^{c})=\frac{1}{2}

(1-P(E))(1-P(F))=\frac{1}{2}\cdots\cdots (2)

From (1) and (2) choice (a) is correct.                        

 


Option 1)

P(E) = 1/3, P(F) = 1/4

Option 2)

P(E) = 1/2, P(F) = 1/6

Option 3)

P(E) = 1/2, P(F) = 1/6

Option 4)

none of these

Posted by

Himanshu

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