Pre-final Practice Score: $28.39 / 31 \quad 30 / 31$ answered Question 19 [0/1 pt $53 \%$ A home pregnancy test was given to women, then pregnancy was verified through blood tests. The following table shows the home pregnancy test results. \begin{tabular}{|r|r|r|r|} \hline & Positive & Negative & Total \\ \hline Pregnant & 52 & 7 & 59 \\ \hline Not Pregnant & 6 & 64 & 70 \\ \hline Total & 58 & 71 & 129 \\ \hline \end{tabular} Round your answers to the nearest thousandth. $P($ positive $\mid$ pregnant $)=$ $P($ pregnant $\mid$ positive $)=$ $P($ negative $\mid$ pregnant $)=$ $P$ (not pregnant $/$ negative $)=$ Submit Question

Step 1 ：Given the table of home pregnancy test results, we are asked to find four probabilities.

Step 2 ：The first probability is the probability of a positive result given that the woman is pregnant. This is a conditional probability and can be calculated by dividing the number of pregnant women who tested positive by the total number of pregnant women. So, \(P(\text{positive} \mid \text{pregnant}) = \frac{\text{number of pregnant women who tested positive}}{\text{total number of pregnant women}} = \frac{52}{59} = 0.881\).

Step 3 ：The second probability is the probability of a woman being pregnant given a positive result. This can be calculated by dividing the number of pregnant women who tested positive by the total number of positive tests. So, \(P(\text{pregnant} \mid \text{positive}) = \frac{\text{number of pregnant women who tested positive}}{\text{total number of positive tests}} = \frac{52}{58} = 0.897\).

Step 4 ：The third probability is the probability of a negative result given that the woman is pregnant. This can be calculated by dividing the number of pregnant women who tested negative by the total number of pregnant women. So, \(P(\text{negative} \mid \text{pregnant}) = \frac{\text{number of pregnant women who tested negative}}{\text{total number of pregnant women}} = \frac{7}{59} = 0.119\).

Step 5 ：The fourth probability is the probability of a woman not being pregnant given a negative result. This can be calculated by dividing the number of non-pregnant women who tested negative by the total number of negative tests. So, \(P(\text{not pregnant} \mid \text{negative}) = \frac{\text{number of non-pregnant women who tested negative}}{\text{total number of negative tests}} = \frac{64}{71} = 0.901\).

Step 6 ：Final Answer: \(P(\text{positive} \mid \text{pregnant}) = \boxed{0.881}\), \(P(\text{pregnant} \mid \text{positive}) = \boxed{0.897}\), \(P(\text{negative} \mid \text{pregnant}) = \boxed{0.119}\), \(P(\text{not pregnant} \mid \text{negative}) = \boxed{0.901}\)