The data shows the number of advanced degrees (in thousands) eamed in a state during a recent year by sex and type of degree. Find the following probabilities for a person selected at random who received an advanced degree. Complete parts (a)-(d). \begin{tabular}{|c|c|c|c|} \hline & Bacholor's & Master's & Doctors \\ \hline Malo & 26 & 62 & 4 \\ \hline Female & 10 & 7 & 0 \\ \hline \end{tabular} (a) The probability that the selected person received a master's degree during the recent year is $\square$. (Type an integer or decimal rounded to three decimal places as needed.) (b) The probability that the selected person is female is $\square$. (Type an integer or decimal rounded to three decimal places as needed) (c) The probability that the selected person is female, given that they received a master's degree during the recent year is $\square$. (Type an integer or decimal rounded to three decimal places as needed.) (d) The probability that the selected person received a master's degree during the recent year given that they are female is $\square$. (Type an integer or decimal rounded to three decimal places as needed.)

Step 1 ：Calculate the total number of people who received an advanced degree. This is the sum of all the numbers in the table. \(Total = 26 + 62 + 4 + 10 + 7 + 0 = 109\) (in thousands)

Step 2 ：The probability that the selected person received a master's degree during the recent year is the sum of the number of males and females who received a master's degree divided by the total number of people. \(P(Master's) = \frac{62 + 7}{109} = \frac{69}{109} = 0.633\)

Step 3 ：\(\boxed{0.633}\) is the probability that the selected person received a master's degree during the recent year.

Step 4 ：The probability that the selected person is female is the sum of the number of females who received a Bachelor's, Master's, or Doctor's degree divided by the total number of people. \(P(Female) = \frac{10 + 7 + 0}{109} = \frac{17}{109} = 0.156\)

Step 5 ：\(\boxed{0.156}\) is the probability that the selected person is female.

Step 6 ：The probability that the selected person is female, given that they received a master's degree during the recent year is the number of females who received a master's degree divided by the total number of people who received a master's degree. \(P(Female | Master's) = \frac{7}{69} = 0.101\)

Step 7 ：\(\boxed{0.101}\) is the probability that the selected person is female, given that they received a master's degree during the recent year.

Step 8 ：The probability that the selected person received a master's degree during the recent year given that they are female is the number of females who received a master's degree divided by the total number of females. \(P(Master's | Female) = \frac{7}{17} = 0.412\)

Step 9 ：\(\boxed{0.412}\) is the probability that the selected person received a master's degree during the recent year given that they are female.