If one discount point costs the borrower 1% of the loan amount, and increases the lender's yield by 1/8th of one percent, how many discount points must be purchased to lower the interest rate by 1%?

Answer (c) the knowledge of how to produce new products;                     (b) a more efficient means of production;

Answer self interest;

Part (a) is relatively straight forward.there are 4 aces in a standard 52-card deck. so the probability that an ace is picked is just 4/52.part (b): note that there are 4 suits in a standard 52-card deck. so picking hearts will be 13/52 or 1/4.part (c): the probability condition or means we need to add the two probabilities because we do not want them simultaneously. so, we end up getting pr(ace) + pr(heart).from part (a), we found that picking an ace had a probability of 4/52, which is reduced down to 1/13.from part (b), we found that picking a heart had a probability of 1/4.so, the probability of an ace or a heart is 1/13 + 1/4 = 4/52 + 13/52 = 17/52.