Home $>$ MATH1001 W - Summer $2023>$ Assessment Pre-final Practice Score: $28.39 / 31 \quad 30 / 31$ answered Progress saved Question 19 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 Total Pregnant & 6 & 64 & 70 \\ \hline \end{tabular} Round your answers to the nearest thousandth. \[ P \text { (positive } \mid \text { pregnant })= \] \[ P(\text { pregnant } \mid \text { positive })= \] $P$ (negative $\mid$ pregnant) $=$

Step 1 ：Given the table of home pregnancy test results, we are asked to find three probabilities: the probability of a positive result given that the woman is pregnant, the probability of being pregnant given a positive result, and the probability of a negative result given that the woman is pregnant.

Step 2 ：We use the formula for conditional probability to calculate these probabilities: \(P(A|B) = \frac{P(A \cap B)}{P(B)}\), where \(P(A|B)\) is the probability of event A given event B is true, \(P(A \cap B)\) is the probability of both events A and B, and \(P(B)\) is the probability of event B.

Step 3 ：From the table, we know that the total number of women is 129, the number of pregnant women is 59, the number of positive results is 58, the number of pregnant women who tested positive is 52, and the number of pregnant women who tested negative is 7.

Step 4 ：Using these numbers, we calculate the probability of a positive result given that the woman is pregnant as \(P(\text{positive} | \text{pregnant}) = \frac{52}{59} \approx 0.881\).

Step 5 ：We calculate the probability of being pregnant given a positive result as \(P(\text{pregnant} | \text{positive}) = \frac{52}{58} \approx 0.897\).

Step 6 ：We calculate the probability of a negative result given that the woman is pregnant as \(P(\text{negative} | \text{pregnant}) = \frac{7}{59} \approx 0.119\).

Step 7 ：Final Answer: \(P(\text{positive} | \text{pregnant}) = \boxed{0.881}\), \(P(\text{pregnant} | \text{positive}) = \boxed{0.897}\), and \(P(\text{negative} | \text{pregnant}) = \boxed{0.119}\).