Question: (3 points)

Lex Luthor wants two pieces of Kryptonite so that he can prevent Superman and Supergirl from defeating him. However, he must find two nuggets (one for Superman and another for Supergirl) because he is unable to break one nugget of Kryptonite into two nuggets because it is extremely strong.

Lex has a mine for mining Kryptonite. It is estimated that he will find 0.95 nuggets of Kryptonite for every cubic kilometre of rock that is mined. Lex's mining equipment can mine 0.24 cubic kilometres of rock per day. Lex will be attacked in 8 days.

What is the probability that Lex will get both nuggets in time to stop the super heroes? (Answer to 2 decimal places)

Assume that Lex finds a nugget to stop Superman. What is the probability that he will also have a nugget to stop Supergirl? (Answer to 2 decimal places)

Assume that Lex has a large number of mines as described above. What is the median amount of time measured in days that it will take a single mine to find two nuggets of Kryptonite? (Answer to 2 decimal places)

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