Assume a stockbroker has suggested eight stocks to the client and that five of the recommended stocks will raise in value over the next year.
(i) Suppose that the client selects to invest in four of the eight recommended stocks at random. Find out the probability that at least half of the stocks chosen by the client will raise in value over the next year. Discuss.
(ii) Suppose that the client will allocate $10,000 to the eight suggested stocks in increments of $1,000, with all allocations (of the $10,000) being equally likely. Find out the probability that the client will only buy stocks that will raise in value over the next year. Explain.