Problem #2
| Planned Vaginal Delivery |
\(b\) |
\(a\) |
\(a+b\) |
| row |
\(\frac{b}{a+b}\) |
\(\frac{a}{a+b}\) |
|
| col |
\(\frac{b}{b+d}\) |
\(\frac{a}{a+c}\) |
|
| Planned Caesarean Section Delivery |
\(d\) |
\(c\) |
\(c+d\) |
| row |
\(\frac{d}{c+d}\) |
\(\frac{c}{c+d}\) |
|
| col |
\(\frac{d}{b+d}\) |
\(\frac{c}{a+c}\) |
|
| All |
\(b+d\) |
\(a+c\) |
\(1\) |
| Table | No Depression | Depression | All |
|-------------------|------------------|------------------|------------------|
| Planned Vaginal Delivery | $b$ | $a$ | $a+b$ |
| row | $\frac{b}{a+b}$ | $\frac{a}{a+b}$ | |
| col | $\frac{b}{b+d}$ | $\frac{a}{a+c}$ | |
| Planned Caesarean Section Delivery | $d$ | $c$ | $c+d$ |
| row | $\frac{d}{c+d}$ | $\frac{c}{c+d}$ | |
| col | $\frac{d}{b+d}$ | $\frac{c}{a+c}$ | |
| All | $b+d$ | $a+c$ | $1$ |
Problem #3
| Planned Vaginal Delivery |
\(b\) |
\(a\) |
\(a+b = 1-g\) |
| row |
\(1-e\) |
\(e\) |
\(1\) |
| col |
\(P(P_V | 1-P_D) =
\frac{(1-P(P_D|P_V))P(P_V)}{1-P(P_D)} =
\frac{(1-e)(1-g)}{b+d}\) |
\(P(P_V|P_D) = \frac{P(P_D|P_V)\cdot
P_V}{P_D} = \frac{e \cdot (1-g)}{(a+c)}\) |
|
| Planned Caesarean Section Delivery |
\(d\) |
\(c\) |
\(c+d = g\) |
| row |
\(1-f\) |
\(f\) |
\(1\) |
| col |
\(P(P_C|1-P_D) =
\frac{(1-P(P_D|P_C))P(P_C)}{1-P(P_D)} =
\frac{(1-f)(g)}{b+d}\) |
\(P(P_C|P_D) = \frac{c}{a+c}\) |
|
| All |
\(b+d\) |
\(a+c\) |
\(1\) |
| Table | No Depression | Depression | All |
|----------------|---------------------------------|-------------------------------------------|----------------|
| Planned Vaginal Delivery | $b$ | $a$ | $a+b = 1-g$ |
| row | $1-e$ | $e$ | $1$ |
| col | $P(P_V | 1-P_D) = \frac{(1-P(P_D|P_V))P(P_V)}{1-P(P_D)} = \frac{(1-e)(1-g)}{b+d}$ | $P(P_V|P_D) = \frac{P(P_D|P_V)\cdot P_V}{P_D} = \frac{e \cdot (1-g)}{(a+c)}$ | |
| Planned Caesarean Section Delivery | $d$ | $c$ | $c+d = g$ |
| row | $1-f$ | $f$ | $1$ |
| col | $P(P_C|1-P_D) = \frac{(1-P(P_D|P_C))P(P_C)}{1-P(P_D)} = \frac{(1-f)(g)}{b+d}$ | $P(P_C|P_D) = \frac{c}{a+c}$ | |
| All | $b+d$ | $a+c$ | $1$ |
Problem #4
| Planned Vaginal Delivery |
\(b = 0.55\) |
\(a=0.15\) |
\(a+b = 1-g = 0.7\) |
| row |
\(1-e\) |
\(e = \frac{0.15}{0.70} =
0.21\) |
\(1\) |
| col |
\(P(P_V | 1-P_D) =
\frac{(1-P(P_D|P_V))P(P_V)}{1-P(P_D)} = \frac{(1-e)(1-g)}{b+d} =
\frac{0.79 \cdot 0.70}{0.75} = 0.74\) |
\(P(P_V|P_D) = \frac{P(P_D|P_V)\cdot
P_V}{P_D} = \frac{e \cdot (1-g)}{(a+c)} = \frac{0.21 \cdot 0.70}{0.25} =
0.59\) |
|
| Planned Caesarean Section Delivery |
\(d = 0.20\) |
\(c=0.10\) |
\(c+d = g = 0.3\) |
| row |
\(1-f = 0.67\) |
\(f = \frac{0.10}{0.3} =
0.33\) |
\(1\) |
| col |
\(P(P_C|1-P_D) =
\frac{(1-P(P_D|P_C))P(P_C)}{1-P(P_D)} = \frac{(1-f)(g)}{b+d} =
\frac{0.67 \cdot 0.3}{0.75} = 0.27\) |
\(P(P_C|P_D) = \frac{c}{a+c} =
\frac{0.10}{0.25} = 0.40\) |
|
| All |
\(b+d = 0.75\) |
\(a+c = 0.25\) |
\(1\) |
| Table | No Depression | Depression | All |
|-----------------|----------------------|-----------------|-----------------|
| Planned Vaginal Delivery | $b = 0.55$ | $a=0.15$ | $a+b = 1-g = 0.7$ |
| row | $1-e$ | $e = \frac{0.15}{0.70} = 0.21$ | $1$ |
| col | $P(P_V | 1-P_D) = \frac{(1-P(P_D|P_V))P(P_V)}{1-P(P_D)} = \frac{(1-e)(1-g)}{b+d} = \frac{0.79 \cdot 0.70}{0.75} = 0.74$ | $P(P_V|P_D) = \frac{P(P_D|P_V)\cdot P_V}{P_D} = \frac{e \cdot (1-g)}{(a+c)} = \frac{0.21 \cdot 0.70}{0.25} = 0.59$ | |
| Planned Caesarean Section Delivery | $d = 0.20$ | $c=0.10$ | $c+d = g = 0.3$ |
| row | $1-f = 0.67$ | $f = \frac{0.10}{0.3} = 0.33$ | $1$ |
| col | $P(P_C|1-P_D) = \frac{(1-P(P_D|P_C))P(P_C)}{1-P(P_D)} = \frac{(1-f)(g)}{b+d} = \frac{0.67 \cdot 0.3}{0.75} = 0.27$ | $P(P_C|P_D) = \frac{c}{a+c} = \frac{0.10}{0.25} = 0.40$ | |
| All | $b+d = 0.75$ | $a+c = 0.25$ | $1$ |
P(Planned caesarean section delivery|Depression score <13) is
\(P(P_C|1-P_D) =
\frac{(1-P(P_D|P_C))P(P_C)}{1-P(P_D)} = \frac{(1-f)(g)}{b+d} =
\frac{0.67 \cdot 0.3}{0.75} = 0.27\)
$P(P_C|1-P_D) = \frac{(1-P(P_D|P_C))P(P_C)}{1-P(P_D)} = \frac{(1-f)(g)}{b+d} = \frac{0.67 \cdot 0.3}{0.75} = 0.27$