There is a 4-in-5 chance that A can complete the marathon. There is a 5-in-8 chance that B can't complete the marathon, which is independent of A's performance. What is the probability that both A and B end up completing?

Probability A completes marathon $= \dfrac{4}{5}$

Probability B can't complete marathon $= \dfrac{5}{8}$

A's and B's performances are independent.

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The problem gives the probability that B can't complete.

$P(B \text{ can't complete}) = \dfrac{5}{8}$

$P(B \text{ can complete}) = 1 - \dfrac{5}{8}$

$P(B \text{ can complete}) = \dfrac{3}{8}$

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Since A and B perform independently:

$P(\text{Both complete}) = P(A \text{ completes}) \times P(B \text{ completes})$

$P(\text{Both complete}) = \dfrac{4}{5} \times \dfrac{3}{8}$

$P(\text{Both complete}) = \dfrac{12}{40}$

$P(\text{Both complete}) = \dfrac{3}{10}$

Therefore, the probability that both A and B complete the marathon is $\dfrac{3}{10}$.