(a) You are trying to decide how best to invest some money that your grandmother gave you for your

birthday. You consult a financial advisor and narrow your options down to two choices. You can either

invest your money in Share A, which is known to be equally likely to yield an annual return anywhere

in the interval between -2% and 15%, or you can put your money in a risk-free savings account which

is guaranteed to produce an annual return of 6.0%. What is the probability that you would be better

off investing in the savings account rather than the share over the next year?

(b) A friend hears of your investment plans outlined in (a) above, and tries to convince you to

diversify your portfolio and invest in 4 shares in addition to Share A above (ie: a total of 5

shares). The forecasted returns for the additional shares are exactly the same as for Share A,

that is they are equally likely to yield an annual return anywhere in the interval between -2%

and 15%. What is the probability that exactly 3 of the 5 shares produce returns greater than

the 6% guaranteed by the savings account?