Question 2 For the random variable described in each situation below, state whether the Binomial distribution would provide a satisfactory model, giving your reasons. If it would, state the values of n and p .

(a) The number of sixes obtained when three dice are thrown simultaneously.

(b) The number of children in a class of 20, whose birthday anniversary falls on a Sunday this year.

(c) The number of tosses required when a one rand coin is tossed until the first head appears.

(d) The number of girl children in the families of US presidents.

(e) The number of 'even numbers' that appear in the winning lotto numbers in a given draw.

Question 3 (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?

Question 4 A manufacturer of glass marbles produces equal large numbers of red and blue marbles. These are thoroughly mixed together and then packed in packets of six marbles which are random samples from the mixture. Two boys, Tom and Vusi, each buy a packet of marbles. Tom prefers the red ones and Vusi the 2 blue ones, so they agree to exchange marbles as far as possible, in order that at least one of them will have six of the colour he prefers. Find the probabilities that, after exchange:

(a) They will both have a set of six of the colour they prefer.

(b) Tom will have four or more blue ones