Q1) Suppose that you want to invest $10,000 in the stock market by buying shares in one of the two companies: A and B. Shares in company A, though risky, could yield a 50% return on investment during the next year. If the stock market conditions are not favourable (i.e., "bear" market), the stock may lose 20% of its value. Company B provides safe investments with 15% return in a "bull" market (market conditions are favourable) and only 5% in a "bear" market. Financial analysts are predicting a 60% chance for a "bull" market and 40% chance for a "bear market". Where should you invest your money? Suppose, rather than relying solely on the financial analysts, you now decide to conduct a more "personal" investigation by consulting a friend who has done well in the stock market. The friend offers the general opinion of "for" or "against" investment quantified in the following manner: If it is a "bull" market, there is a 90% chance the vote will be "for". If it is a "bear" market, the chance of a "for" vote is lowered to 50%. How do you make use of this additional information. Hint: The formula given below will provide you some help in solving the above problem. You can also solve the above question if your conception of joint probability, marginal probability and total probability is clear. P(AB)=P(B)P(BA)P(A)