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By class of travel, the two-way table provides information on adult passengers who lived and died. Let's say we pick a random adult passenger.

The number of favorable outcomes divided by the total number of possible outcomes equals probability. As a result, the following is a definition of condition probability:$P(A/B)=\frac{P(AandB)}{P\left(B\right)}$

The person is chosen first class, according to the question. Now we need to figure out how likely it is that "he or she survived."

Therefore,

$P(Firstclassandsurvive)=\frac{favorableoutcomes}{possibleoutcomes}=\frac{197}{1207}$

$P(Firstclass)=\frac{favorableoutcomes}{possibleoutcomes}=\frac{197+122}{1207}=\frac{319}{1207}$

As a result, the conditional probability is:

$$\begin{gathered} P(survived/Firstclass)=\frac{P(Firstclassandsurvived)}{P(Firstclass)} \\ P(survived/Firstclass)=\frac{{\displaystyle \frac{197}{1207}}}{{\displaystyle \frac{319}{1207}}} \\ P(survived/Firstclass)=\frac{197}{319} \\ P(survived/Firstclass)鈮�0.6167 \end{gathered}$$

As a result, the likelihood of the conclusion "he or she survived" is

$P(survived/Firstclass)=0.6167$

The person is chosen for survival based on the question. Now we need to figure out how likely it is that "he or she was a third-class traveler" was the case. Therefore,

$P(Thirdclassandsurvive)=\frac{favorableoutcomes}{possibleoutcomes}=\frac{151}{1207}$

$$\begin{gathered} P(Firstclass)=\frac{favorableoutcomes}{possibleoutcomes}=\frac{197+94+151}{1207} \\ P(Firstclass)=\frac{442}{1207} \end{gathered}$$

As a result, the conditional probability is:

$$\begin{gathered} P(Thirdclass/survived)=\frac{P(Thirdclassandsurvived)}{P(Firstclass)}=\frac{{\displaystyle \frac{151}{1207}}}{{\displaystyle \frac{442}{1207}}} \\ P(Thirdclass/survived)=\frac{151}{442}鈮�0.3416 \end{gathered}$$

As a result, the likelihood of the finding "he or she was a third-class traveler" is high.

$P(Thirdclass/survived)=0.3416$