3. Collecting Bears 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 Dea buys one box of this cereal each week. Let Tl be the number of weeks it takes for Dea to get her first bear. Let Tm be the number of weeks it takes for Dea to get her tenth bear. Find the following probabilities. In each part, first write a math expression for the chance. If you have any infinite sums in your expression, please be sure to simplify them. Then use the code cell at the end of the exercise to find the numerical value. Remember that you can use stats .binom.pmf for binomial probabilities, and stats.binom.cdf forthe binomial cdf. Provide the numerical value along with your math expression. a)P(T1 > 12) blP(T10 = 40) c) P(T10 > 40) d) P(T]0 > 40 | T1 = 8) # code cell for Exercise 3 numerical calculations