the number of people who survived the titanic based on class and gender is in the following table. suppose a…
the number of people who survived the titanic based on class and gender is in the following table. suppose a person is picked at random from the survivors.\n| class | female | male | total |\n| 1st | 134 | 60 | 194 |\n| 2nd | 93 | 24 | 117 |\n| 3rd | 81 | 57 | 138 |\n| total | 308 | 141 | 449 |\na) what is the probability that a survivor was male?\nround final answer to 3 decimal places.\nb) what is the probability that a survivor was in the 3rd class?\nround final answer to 3 decimal places.\nc) what is the probability that a survivor was a male given that the person was in 3rd class?\nround final answer to 3 decimal places.
Answer
Explanation:
Step1: Recall probability formula
The probability formula is $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of elements in event $A$ and $n(S)$ is the number of elements in the sample - space.
Step2: Calculate probability for part a
The total number of survivors $n(S)=449$, and the number of male survivors $n(A) = 141$. So $P(\text{male})=\frac{141}{449}\approx0.314$.
Step3: Calculate probability for part b
The number of 3rd - class survivors $n(A)=138$, and $n(S) = 449$. So $P(\text{3rd class})=\frac{138}{449}\approx0.307$.
Step4: Calculate probability for part c
The number of 3rd - class male survivors $n(A)=57$, and the number of 3rd - class survivors $n(S)=138$. So $P(\text{male}|\text{3rd class})=\frac{57}{138}\approx0.413$.
Answer:
a) $0.314$ b) $0.307$ c) $0.413$