1 a) Find the probability of throwing a sum of 3 at least 6 times in 12 throws of a pair of fair dice

1b)

A $80000 oil detector is lowered under the sea to detect oil fields, and it becomes detached from the ship. If the instrument is not found within 36 hours, it will crack under the pressure of the sea. It is assumed that a SCUBA diver will find it with probability 0.75, but it costs $ 700 to hire each diver.

a)How many SCUBA divers should be hired in order to maximize the expected gain? answer: (round to nearest integer)

b)Using your answer to part a), what is the expected gain? answer: $