A salesman has scheduled two appointments to sell encyclopedias. His first appointment will lead to a sale with probability .3, and his second will lead independently to a sale with probability .6. Any sale made is equally likely to be either for the deluxe model, which costs \$1000, or the standard model, which costs \$500. Determine the probability mass function of X, the total dollar value of all sales.
There are a few scenarios which we should consider. The possibility that the salesman sells no encyclopedias, the \$500 encyclopedia, or the \$1000 encyclopedia. So there are $3^2=9$ different ways to make these sells. The possible scenarios for selling to the first and second customer looks like,
where our random variable X is the sum of the sales to the first and second customer
F = first appointment sale
S = second appointment sale
$F_1$= sale of \$500 on first appt
$F_2$= sale of \$1000 on first appt
$S_1$= sale of \$500 on second appt
$S_2$= sale of \$1000 on second appt
consider a few,
$$P(X=0)=P(F^c \cap S^c)=P(F^c)P(S^c)=(1-0.3)(1-0.6)=0.28$$
continue after this manner to find P(X=1000), P(X=1500), P(X=2000) making sure your probabilities sum to 1.
Surround your text in
**bold**, to write a math equation use, for example,