Q1) Assume a professor arbitrarily chooses 3 new teaching assistants from the total of 20 applicants-12 male and 8 female students. Let X be number of females who are hired. 

i) Determine the probability that no female are hired.

ii) Determine the mean and standard deviation of X. 

Q2) In testing lethal concentration of chemical found in polluted water, it is determined that certain concentration will kill 40% of fish which are subjected to it for 24 hours. If 5 fish are placed in the tank concentration of chemical, determine the probability that after 24 hours.

i)  Exactly 4 survive

ii) At least 4 survive   

iii) At most 1 survives.