A probability class consists of 20 students, unimaginatively called Student 1, Student 2, and so on.

a) Student 1 rolls a die 12 times. Write a math expression for the chance that Student 1 gets 2 sixes. Use the code cell below to write a Python expression that evaluates to the chance, and then write the output on your paper along with the math expression. You don't have to write all the decimal places. Just four or five places is fine, and don't worry about exactly how to round.

b) Each of the 20 students rolls 12 dice. Write a math expression for P(at least one of the students gets 2 sixes)P(at least one of the students gets 2 sixes). You will need the answer to part a but you don't have to rewrite it. Just call it pp.

The numerical value of pp is ans_1a above. Use the code cell below to find the numerical value of P(at least one of the students gets 2 sixes)P(at least one of the students gets 2 sixes) and write the output on your paper along with the math expression.

c)

c) Suppose instead the students proceed as follows:

Student 1 rolls a die 12 times. If 2 sixes appear, the experiment is over. If not, then
Student 2 rolls a die 12 times. If 2 sixes appear, the experiment is over. If not, then
Student 3 rolls a die 12 times. If 2 sixes appear, the experiment is over. If not, then
Student 4 rolls 12 dice ...
And so on.

Write a math expression for the chance that Student 5 is the first student who sees 2 sixes.

Use the code cell below to find the numerical value of the chance and write it on your paper along with your expression.