Question

A speaks truth in 75% of the cases and B in 80% of the cases. The percentage of cases they are likely to contradict each other in making the same statement is ______.

Options

• 25%

• 35%

• 50%

• 65%

Answer 1

A speaks truth in 75% of the cases and B in 80% of the cases. The percentage of cases they are likely to contradict each other in making the same statement is 35%.

Explanation:

E: Event that A and B contradict in making the same state statement.

∴ E = `(A ∩ barB) ∪ (barA ∩ B)`

P(E) = `P((A ∩ barB) ∩ (barA ∪ B))`

= `P(A ∩ barB) + P(barA ∩ B)`

= `P(A)P(barB) + P(barA).P(B)`

= `75/100 xx 20/100 + 25/100 xx 80/100`

= `3/4 xx 1/5 + 1/4 xx 4/5`

= `7/20 xx 100%`

= 35%