Question

)sanjay, ekansh and naman are three friends. sanjay speaks truth 3 out of 4 times, ekansh speaks truth 4 out of 5 times while na man speaks truth 3 out of 5 times what is the probability that atleast one of them narrates an incident truthfully?

Answer 1

P(Sanjay speaks the truth) = 3/4

P(Sanjay does not speak the truth) = 1- 3/4 = 1/4

P(Ekansh speaks the truth) = 4/5

P(Ekansh does not speak the truth) = 1- 4/5 = 1/5

P(Naman speaks the truth) = 3/5

P(Naman does not speak the truth) = 1- 3/5 = 2/5

Find the probability that none speak the truth:

P(All three do not speak the truth) = (1/4)(1/5)(2/5) = 1/50

Find the probability that at least 1 speaks the truth:

P(at least 1 speaks the truth) = 1 - 1/50 = 49/50 or 98%

Answer: The probability of at least one of them speaks the truth is 90%