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` speaks truth
then ,`P(A_(1))=60//100=3//5,P(A_(2))=70//100=7//10` for the required event either both of then should
Speck the truth or both of them should tell a lie
thus , the required probaility is
`P((A_(1)nnA_(2))cup(barA_(1)nnbarA_(2)))`
`=p(barA_(1)nnA_(2))+P(barA_(1)nnbarA_(2))`
`=P(A_(1))P(A_(2))+P(barA_(1)nn barA_(2))`
` =P(A_(1))P(A_(2))+P(barA_(1))P(barA_(2))`
`(3)/(5)xx(7)/(10)+(1-(3)/(5))(1-(7)/(10))`
`=0.54`