AP EAMCET202124 Aug 2021Evening ShiftMathematicsProbabilityActual
A box contains n coins, m of which are fair and the rest are biased. When a biased coin is tossed, the probability of getting a head is twice as likely as tail. A coin is drawn from the box at random and is tossed twice. It is found that first time it shows head and the second time it shows tail. Then, the probability that the coin drawn is fair is
Options
- A7 m 8 n+m
- B9 m 8 n+m
- C7 m 8 m+n
- D9 m 8 m+n
Correct answer
B. 9 m 8 n+m
Step-by-step solution
Let the event A and BA= fair coin tossed B= biased coin tossed E= first time head second time tail P(A)= m n , P(B)= n-m n P(E / A)= 1 4 , P(E / B)= 2 9 Required probability P(A / E)= P(A) P(E / A) P(A) P(E / A)+P(B) P(E / B) = m n 1 4 m n 1 4 + n-m n ( 2 9 ) = 9 m 9 m+8 n-8 m = 9 m 8 n+m