Question

Dinesh and Virat both speak truth with probability ⅕ and speak lie with probability ⅘. Dinesh watched a football match and had a conversation with Virat about the result. Virat had further conversation with Rohan, “Dinesh told me that Brazil won”. What probability should Rohan assign to Brazil’s win?
a. 13/25
b. 12/25
c. 7/25
d. 17/25

Answer 1

Answer:

17/25 is the most suitable one

Answer 2

Given:

1. Probability of speak truth by Dinesh and Virat P(S) = ⅕
2. Probability of speak a lie by Dinesh and Virat  P(L) =  ⅘
3. Dinesh spoke to Virat who then spoke to Roshan that Brazil won.

To find:

1. Probability that Brazil won.

Answer:

• Let, P(BW) denote the probability that Brazil won and P(BL) denote the probability that Brazil lost.
• Probability that Brazil won = Brazil won and Dinesh and Virat both speak the truth + Brazil won and Dinesh and Virat both speak lie.
• P(BW) = [ P(S) × P(S) ] + [ P(L) × P(L) ]
• P(BW) = $\frac{1}{5 * 5} +\frac{4 * 4}{5 * 5}$ = 17 / 25

Thus the, probability that Rohan should assign to Brazil’s win = d. 17/25