David Barnes and his fianc$$e Valerie Shah are visiting Hawaii. There are $30$ guests registered for orientation. It is announced that $13$ randomly selected registered guests will receive a free lesson of the Tahitian dance.

a$.$ What is the probability that both David and Valerie get picked for the Tahitian dance lesson? $($Round your answer to $4$ decimal places.$)$

Answer is complete and correct.

Probability

b$.$ What is the probability that neither of them gets picked for the Tahitian dance lesson? $($Round your answer to $4$ decimal places:$)$

Answer is complete but not entirely correct.

$\backslash$table$[[$Probability$,0\mathrm{.}8207.]]$