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.

a) 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,
• the * symbol, and
• 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.