Chi Squared Goodness of Fit Test and Probability

One year, at England University, there were these FOUR students who were taking Chemistry and who did pretty well on all of the quizzes and labs. These students were so confident that they decided to party the weekend before their final exams. They partied and drank alcohol, which resulted in them sleeping all day Sunday and waking up late on the Monday morning of their final examination. Rather than attend the exam, they arrived after the exam and explained to their professor why they were late and had missed the exam. They told him they went away and on the way back home they had a flat tyre with no spare tyre to fix it. The professor agreed and let them sit their examination the very next day, but they were shocked upon finding their very first question in the exam. It said: Which tyre?

1) There are 44 different ways in which the four students could have answered this question.
 What is the probability that the four students passed the chemistry examination?

2) A statistician and a mathematician were arguing over the validity of the
above probability calculation. The statistician felt the calculation was
valid because she felt each tyre was equally likely to be picked. The
mathematician felt students were twice as likely to pick a front tyre over
a rear tyre going flat, because many would think that the front tyres are
more likely to run over something first that could damage a tyre. The
statistician decided to settle the argument by surveying 40 students from
her class. The following results were obtained (REFER TO ATTACHMENT)

Perform a chi-squared goodness of fit test, using a 0.05 significance level,
to see if the data supports the statistician’s hypothesis.

3) The mathematician claimed the data clearly confirmed his argument as
almost twice an many students picked the front tyre. Conduct another
chi-squared goodness of fit test with a 0.05 significance level to see if the
data supports the mathematician’s point of view.

4) Given your results from above, what conclusion can be made?

Please show all working, thank you