First, we need to calculate the probability of drawing a red ball the first time. This is given by the usual probability:
[tex]P_{\text{red}1}=\frac{\text{red }}{total}=\frac{8}{11}[/tex]Now, as for the second time we pick a ball. Notice that the number of balls in the bag has changed since there is 1 red ball less. So, the probability of extracting a red ball under these conditions is:
[tex]P_{\text{red}2}=\frac{red}{\text{total}}=\frac{7}{10}[/tex]Notice that now the total number of balls is 10 and there are 7 red ones.
Finally, the probability we are looking for is given below:
[tex]P_{\text{red}1}\cdot P_{\text{red}2}=\frac{8}{11}\cdot\frac{7}{10}=\frac{56}{110}\approx0.50909\ldots\approx0.51[/tex]The probability is the above expression, in case you need it expressed as a fraction or a decimal number.