1) In a football (soccer) team consisting of 11 players, 6 are right-footed, 3 are left-footed and 2 are two-footed (ie. equally good with their right and left legs). In preparation for a penalty shoot-out, the team manager has to select a group of 5 (different) players. The manager decides to do this at random.
1.a) What is the probability that the selected five players are all right-footed?
1.b) What is the probability that two or more selected players are not right-footed?
1.c) Assuming that players were chosen one after the other, what is the probability that both the first and the last (i. e. the fifth) selected players are right-footed?
2) Stockpiling medical masks is an important task of any government during the corona outbreak. Regrettably, not all masks producers meet the same quality standards. A certain government has a current stockpile of millions of mask, 60% of which were produced by factory F1 and 40% by factory F2. It is estimated that 1 out of every 100 masks produced by F1 are substandard, whereas 1 out of every 40 masks produced by F2 are substandard.
Answer the following questions by defining relevant events and stating the properties/principles that you apply:
2.a) What is the probability that a mask stockpiled by the government is substandard?
2.b) What is the probability that a non-substandard mask in the government’s stockpile was produced by factory F2?