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JEE Advanced2011MathematicsProbabilityActual

Let E and F be two independent events. The probability that exactly one of them occurs is 11 / 25 and the probability of none of them occurring is 2 / 25 . If P(T) denotes the probability of occurrence of the event T , then

Options

  1. AP(E)= 4 5 , P(F)= 3 5
  2. BP(E)= 1 5 , P(F)= 2 5
  3. CP(E)= 2 5 , P(F)= 1 5
  4. DP(E)= 3 5 , P(F)= 4 5

Correct answer

A. P(E)= 4 5 , P(F)= 3 5

Step-by-step solution

P(E F)-P(E F)= 11 25 (i.e. only E or only F ) Neither of them occurs = 2 25 P( E F )= 2 25 From Eq. (i), we get P(E)+P(F)-2 P(E F)= 11 25 From Eq. (ii), we get gathered (1-P(E))(1-P(F))= 2 25 1-P(E)-P(F)+P(E) P(F)= 2 25 gathered (iv) From Eqs. (iii) and (iv), we get aligned & P(E)+P(F)= 7 5 and P(E) P(F)= 12 25 & P(E) 7 5 -P(E) = 12 25 aligned aligned & (P(E))^2- 7 5 P(E)+ 12 25 =0 & (P(E)- 3 5 ) (P(E)- 4 5 )=0 & P(E)= 3 4 or 4 5 P(F)= 4 5 or 3 5 aligned

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