Given the table below showing the
joint probability distribution of variables x and y.
[tex]\begin{tabular}
{|c|c|c|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}[/tex]
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
