Testosterone (T) is the naturally occurring male hormone produced primarily in the testes. Epitestosterone (E) is an inactive form of testosterone that may serve as a storage substance or precursor that gets converted to active T. The normal urinary range for the T/E ratio for any person has been set to scientists to be 6:1. That means that 99% of normal men will have that or lower and 1% will have higher than that. By normal we mean not doping on testosterone. Testing for doping is commonly done to athletes. If an athlete is tested and it is found to have a T/E ratio larger than 6:1 it is accused of doping. Four athletes from a team of 11 soccer players are sampled at random to determine whether they are doping. They are given the test to determine their T/E ratio. (a) List the sample space of this sampling experiment (where 1= T/E ratio > 6:1, 0 =the complement event). Show the whole listing. (b) Let A be the event that 2 of the four test positive for doping. Calculate the probability of event A. Show work. (c) Put together a table in which in one column you put X, which can take values 0, 1, 2, 4, where 0 means there are 0 in the sample of 4 are determined by the test to be doping; 1 means that there is one one in the sample of four that is determined to be doping, etc. In the second column, put the probability of finding 0 doping among the four, the probability of finding 1 doping among the four, and so on. Complete the table. Since you showed work to calculate part (b) you can just show the final numbers in this part (c). But notice that wrong single numbers without work can not give partial credit. Add , when done completing the table, the formula that represents this probability table you found. (d) Are you surprised by the results, given the information we are given? What information would be needed to obtain higher probabilities in the table? Explain.