A speaks truth in 605 cases and `B` speaks truth in 70% cases. The probability that they will say the same thing while describing a single event is `2//19` b. `3//29` c. `17//19` d. `4//29`

Options

A. `0.56`
B. `0.54`
C. `0.38`
D. `0.94`

Answer

B

Explanation

Consider the following events:
`A_(1):A` speaks truth
`A_(2):B` speask truth
Then, `P(A_(1)) =60//100=3//5,P(A_(2))=70//100=7//10.`
For the required event, wither both of them should speak the truth of both of them should tell a lie. Thus, the required probability is
`=P((A_(1)nnA_(2))uu(barA_(1)nnbarA_(2))`
`=P(A_(1)nnA_(2))+P(barA_(1)nnA_(2))+P(barA_(1)nnA_(2))`
`=P(A_(1))P(A_(2))+P(barA_(1))(barA_(2))`
`=3/5xx7/10+(1-(7)/(10))=0.54`