. The probability that two specified letters will be placed in the correct envelopes is 1[n(n – 1)]. The probability that none of the othern – 2 letters will then be placed in the correct envelopes is qn-2. Therefore, the probability that only the two specified letters, and no other letters, will be placed 1 in the correct envelopes is It follows that the probability that exactly two of the n n(n – 1) letters will be placed in the correct envelopes, without specifying which pair will be correctly placed,

Suppose that in a certain large population, the proportion of people that have blood type O is 0.33. If 7 people are randomly and independently selected from this population, what is the probability that no more than one has blood type O? (Give your response to at least 3 decimal places. Give only your numeric response, and not any extra characters or symbols.) Your Answer:

Computers A and B can independently generate positive integers: • Computer A generates positive integer n with probability a/3", where a is a constant. • Computer B generates positive integer n with probability 3/n!, where ß is a constant. (a) Find the probability that the number generated by A is larger than the number generated by B. (b) Find the probability that the number generated by A is smaller than the number generated by B.

Each of the numbers 0 - 9 is written on a sheet of paper and the ten sheets of paper are placed in a box If two of these sheets of paper are selected from the box at random, without replacement, find the probability that both numbers are greater than 7.