Answer
$P(survived~|~male)=\frac{338}{1690}=0.2$
Work Step by Step
- First, we need to find $P(male)$:
1) a single event
2) relative frequency
Use the Empirical Approach (page 258):
The sample space: 2224 passengers. So, $N(S)=2224$
According to the marginal distribution (see page 235) of the first column: $N(male)=1690$
$P(male)=\frac{N(male)}{N(S)}=\frac{1690}{2224}$
- For $P(survived~and~male)$ use relative frequency: Empirical Approach (page 258):
According to the cell in the first row, first column: $N(survived~and~male)=338$
$P(survived~and~male)=\frac{N(survived~and~male)}{N(S)}=\frac{338}{2224}$
- Now, use the Conditional Probability Rule (page 288):
$P(survived~|~male)=\frac{P(survived~and~male)}{P(male)}=\frac{\frac{338}{2224}}{\frac{1690}{2224}}=\frac{338}{1690}=0.2$
