A cereal company puts a small plastic bear in some of its cereal boxes. Customers who collect 10 of these bears win a grand prize.

Suppose that each box contains a bear with chance 1/5, independently of all other boxes. Suppose also that Rohan buys one box of this cereal each week.

Let T1T1 be the number of weeks it takes for Rohan to get his first bear.
Let T10T10 be the number of weeks it takes for Rohan to get his tenth bear.

Find the following probabilities. In each part, first write a math expression for the chance, and then use the code cell at the end of the exercise to find the numerical value. Provide the numerical value along with your math expression.

(a) P(T1>12)P(T1>12)
(b) P(T10=40)P(T10=40)
(c) P(T10>40)P(T10>40)
(d) P(T10>40∣T1=8)