1. Monkey Dialing 911 Route, a baby Capuchin monkey in Southern California, managed to call 911 on a cell phone. Nobody is quite sure how Route did this, but let's see what the probabilities look like if we make up some assumptions. 3) Suppose a cell phone screen has Call button as well as a grid of 12 buttons consisting of - one each for the 10 digits 0 through 9, o the * symbol, and o the # symbol. Suppose that each time a monkey presses a button on this screen, it has a 70% chance of picking the brightly colored Call button and a 30% chance of picking at a button at random from the other 12 buttons, independent of its choices at all other times. What is the chance that the first four buttons the monkey presses are 9, 1, 1, Call, in that order? Write the arithmetic expression on paper (not in code) and provide its numerical value. You can use the code cell below, or a calculator, or any such computational device. We will not grade your code. # Calculation for 1a b) Now suppose each of 500 monkeys has a cell phone screen just like the one in Part a, and each monkey presses the buttons under the assumptions of Part 3 independently of all other monkeys. What is the chance that at least one of the 500 monkeys chooses 9, 1, 1, Call (in that order) as the first four buttons to press? As in Part a, write the arithmetic expression on paper and then find its numerical value. # Calculation for 1h