A speaks the truth in 70% of cases and B lies in 40% of cases. The probability that they will say the same thing while describing a single event (to have occurred or not) will be:

A speaks the truth in 70% of cases, so A lies in 30% of cases.

B lies in 40% of cases, so B speaks the truth in 60% of cases.

Therefore:

• P(A tells truth) = $\frac{7}{10}$
• P(A lies) = $\frac{3}{10}$
• P(B tells truth) = $\frac{3}{5}$
• P(B lies) = $\frac{2}{5}$

For A and B to say the same thing while describing a single event, either both tell the truth or both lie.

P(Both tell truth) = P(A tells truth) × P(B tells truth)

$= \frac{7}{10} \times \frac{3}{5}$

$= \frac{21}{50}$

P(Both lie) = P(A lies) × P(B lies)

$= \frac{3}{10} \times \frac{2}{5}$

$= \frac{6}{50}$

P(They say the same thing) = P(Both tell truth) + P(Both lie)

$= \frac{21}{50} + \frac{6}{50}$

$= \frac{27}{50}$

Therefore, the probability that they will say the same thing is $\frac{27}{50}$.