A man speaks truth ( 2 ) out of ( 3 ) times. He picks one of the natural numbers in the set ( S= 1,2, ), ( 3,4,5,6,7 ) and reports that it is even. The probability that it is actually even is

Step-by-step solution

S = 1,2,3,4,5,6,7 E₁= An even number is picked, E₂= An odd number is picked P (E₁ )= 3 7 , P (E₂ )= 4 7 E: A man reports an even number P (E E₁ )= 2 3 P (E E₂ )= 1 3 Required probability =P (E₁ E )= P (E E₁ ) P (E₁ ) P (E E₁ ) P (E₁ )+P (E E₂ ) P (E₂ ) = ( 2 3 ) ( 3 7 ) ( 2 3 ) ( 3 7 )+ ( 1 3 ) ( 4 7 ) = 6 6+4 = 3 5