Question

The joint probability distribution of variables x and y is shown in the table below. rebecca and rachel are car salespeople. let x denote the number of cars that rebecca will sell in a month, and let y denote the number of cars rachel will sell in a month. what is the probability that rachel and rebecca will combine to sell 3 cars in one month?

Answer 1

Given the table below showing the joint probability distribution of variables x and y.


`\begin{tabular} c \multicolumn{4}c{X}\\ Y&1&2&3\\ 1&0.30&0.18&0.12\\ 2&0.15&0.09&0.06\\ 3&0.05&0.03&0.02 \end{tabular}`

Given that x denote the number of cars that Rebecca will sell in a month, and y denote the number of cars Rachel will sell in a month.

If Rachel and Rebecca combine to sell 3 cars in one month, then it is either Rachel will sell 2 cars and Rebecca will sell 1 car or Rachel will sell 1 car and Rebecca will sell 2 cars.

The probability that Rachel and Rebecca combine to sell 3 cars in one month is given by the sum of the probability that Rachel will sell 2 cars and Rebecca will sell 1 car and the probability that Rachel will sell 1 car and Rebecca will sell 2 cars.

The probability that Rachel will sell 2 cars and Rebecca will sell 1 car is 0.15 and the probability that Rachel will sell 1 car and Rebecca will sell 2 cars is 0.18.

Therefore, the probability that Rachel and Rebecca combine to sell 3 cars in one month is 0.15 + 0.18 = 0.33