An envelope is known to have come from either 'LONDON' or 'CLIFTON'. On the postal mark only two successive letters ON are legible. The probability that the envelope comes from LONDON is

Step-by-step solution

According to the given information, the number of two successive letters in word LONDON is 5, similarly in word CLIFTON is 6. Let event E₁ is selecting word LONDON and event E₂ is selecting word CLIFTON. So, P (E₁ )= 1 2 and P (E₂ )= 1 2 and the event A is getting successive letter ON. Then, P (A / E₁ )= 2 5 and P (A / E₂ )= 1 6 . Required probability, P ( E₁ A )= P (E₁ ) P ( A E₁ ) P (E₁ ) P ( A E₁ )+P (E₂ ) P ( A E₂ ) aligned & = 1 2 2 5 ( 1 2 2 5 )+ ( 1 2 1 6 ) = 2 5 2 5 + 1 6 & = 2 6 12+5 = 12 17 aligned Hence,