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. Also, suppose that you buy one box of this cereal each week. Let W1 be the number of weeks it takes for you to get his first bear, and W2 be the number of weeks it takes for you to get your tenth bear. Find the following probabilities. In each part, writing a math expression for the chance is enough. That means, you do not have to calculate the expression and give a numeric value as the answer. However, you need to simplify the expressions as possible as you can.

(a) [1pt] P(W1 = 10)

(b) [1pt] P(W1 > 10)

(c) [1pt] P(W2 = 50)

(d) [1pt] P(W2 > 50)

(e) [1pt] P(W2 > 50|W1 = 10)