In a large corporation, 65% of the employees are male. A random sample of 5 employees is selected. We wish to determine the probability of selecting exactly 3 males. Use an appropriate probability distribution to answer the following:  (a) Define the variable of interest for this scenario.                                                (b) What is the probability that the sample contains exactly three male employees?   (c) Justify the suitability of the probability distribution that you used to solve part (a).  (d) What is the expected number of male employees in the sample?

All human blood can be "ABO-typed" as one of O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in a country. Blood type A National probability 0.43 0.12 AB ? (a) What is the national probability of type AB blood? O 0.41 (b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen person from this country can donate blood to Maria?

If you have a sample of 100 patients at a hospital and 20 of them have the flu, what is the probability Of randomly selecting 3 patients in a row who have the flue?

In Alpha College, students are required to join at least one school club to get extra-curriculum activities’ marks.Suppose the following table represents the probability distribution function of the number of clubs (?) astudent join: ?  1  2 3 4 ?(? = ?)  0.1  2?   ? + 0.1  ? (a) Find the value of ?.(b) What is the probability that a student joins at most two clubs?(c) Find ?(?), ???(?) and ?(?).(d) Suppose the membership fee is $100 per club, with the first enrolled club is free of charge. Let ? bethe total membership fee a student pay. Compute ?(?) and ?(?).(e) What percentage of students are paying not less than $200 for the total membership fee?(f) Write a simple paragraph (about 30 -50 words) to summarize the total membership fee a student payingfor joining school club(s) (based on the results in parts (d) and (e)).