Question

The Titanic struck an iceberg and sank on its first voyage across the Atlantic in 1912. Some passengers got off the ship in lifeboats, but many died.

Two-way tables
ANSWERED
asked 2020-12-24
The Titanic struck an iceberg and sank on its first voyage across the Atlantic in 1912. Some passengers got off the ship in lifeboats, but many died. The two-way table gives information about adult passengers who survived and who died, by class of travel.
\(\begin{array}{c|c} & First & Second & Third \\ \hline Yes & 197 & 94 & 151\\ \hline No & 122 & 167 & 476\\ \end{array}\)
Suppose we randomly select one of the adult passengers who rode on the Titanic. Given that the person selected was in first class, what's the probability that he or she survived?

Answers (1)

2020-12-25
DEFINITIONS
Definition conditional probability:
\(P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{P(A \text{ and } B)}{P(A)}\)
SOLUTION
\(\begin{array}{c|ccc|c} & First & Second & Third &Total\\ \hline Yes & 197 & 94 & 151&442\\ No & 122 & 167 & 476&765\\ \hline Total & 319 & 261 & 627 & 1207 \end{array}\)
F=First class
S=Survived
We note that the table contains information about 1207 passengers (given in the bottom right corner of the table).
Moreover, 319 of the 1207 passengers are first class passengers, because 319 is mentioned in the row *Total” and in the column *First” of the table. The probability is the number of favorable outcomes divided by the number of possible outcomes:
\(P(F)=\frac{\# \text{ of favorable outcomes}}{\# \text{ of possible outcomes}}=\frac{319}{1207}\) Next, we note that 197 of the 1207 passengers are first class passengers that survived, because 197 is mentioned in the row ”Yes” and in the column ” First” of the given table.
\(P(F \text{ and } S)=\frac{\# \text{ of favorable outcomes}}{\# \text{ of possible outcomes}}=\frac{197}{1207}\)
Use the definition of conditional probability:
\(P(S|F)=\frac{P(F \text{ and } S)}{P(F)}=\frac{\frac{197}{1207}}{\frac{319}{1207}}=\frac{197}{319}\approx0.6176=61.76\%\)
Answer:\(\frac{197}{319}\approx0.6176=61.76\%\)
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-02-12
In 1912 the Titanic struck an iceberg and sank on its first voyage. Some passengers got off the ship in lifeboats, but many died. The following two-way table gives information about adult passengers who survived and who died, by class of travel.
\(\begin{array} {lc} & \text{Class} \ \text {Survived } & \begin{array}{c|c|c|c} & \text { First } & \text { Second } & \text { Third } \\ \hline \text { Yes } & 197 & 94 & 151 \\ \hline \text { No } & 122 & 167 & 476 \end{array}\ \end{array}\)
Suppose we randomly select one of the adult passengers who rode on the Titanic. Define event D as getting a person who died and event F as getting a passenger in first class. Find P(not a passenger in first class or survived).
asked 2021-01-30
In 1912 the luxury liner Titanic struck an iceberg and sank. Some passengers got off the ship in lifeboats, but many died. The two-way table gives information about adult passengers who survived and who died, by class of travel. Check the conditions for performing a chisquare test for association.
\(\begin{array}{l|c|c|c|c} & \text { First } & \text { Second } & \text { Third } & \text { Total } \\ \hline \text { Survived } & 197 & 94 & 151 & 442 \\ \hline \text { Died } & 122 & 167 & 476 & 765 \\ \hline \text { Total } & 319 & 261 & 627 & 1207 \\ \end{array}\)
asked 2021-07-01

In 1912 the Titanic struck an iceberg and sank on its first voyage. Some passengers got off the ship in lifeboats, but many died. The following two-way table gives information about adult passengers who survived and who died, by class of travel.

\(\begin{array} {lc} & \text{Class} \\ \text {Survived} & \begin{array}{c|c|c|c} & \text { First } & \text { Second } & \text { Third } \\ \hline \text { Yes } & 197 & 94 & 151 \\ \hline \text { No } & 122 & 167 & 476 \end{array}\ \end{array}\)

Suppose we randomly select one of the adult passengers who rode on the Titanic. Define event D as getting a person who died and event F as getting a passenger in first class. Find P (not a passenger in first class and survived).

asked 2021-06-13
1. Who seems to have more variability in their shoe sizes, men or women?
a) Men
b) Women
c) Neither group show variability
d) Flag this Question
2. In general, why use the estimate of \(n-1\) rather than n in the computation of the standard deviation and variance?
a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation
b) The estimate n-1 is never used to calculate the sample variance and standard deviation
c) \(n-1\) provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population
d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.
\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 25.7 & M \\ \hline 25.4 & F \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 26.7 & M \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 25.4 & F \\ \hline 25.7 & M \\ \hline 25.7 & F \\ \hline 23.5 & F \\ \hline 23.1 & F \\ \hline 26 & M \\ \hline 23.5 & F \\ \hline 26.7 & F \\ \hline 26 & M \\ \hline 23.1 & F \\ \hline 25.1 & F \\ \hline 27 & M \\ \hline 25.4 & F \\ \hline 23.5 & F \\ \hline 23.8 & F \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline \end{array}\)
\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 27.6 & M \\ \hline 26.9 & F \\ \hline 26 & F \\ \hline 28.4 & M \\ \hline 23.5 & F \\ \hline 27 & F \\ \hline 25.1 & F \\ \hline 28.4 & M \\ \hline 23.1 & F \\ \hline 23.8 & F \\ \hline 26 & F \\ \hline 25.4 & M \\ \hline 23.8 & F \\ \hline 24.8 & M \\ \hline 25.1 & F \\ \hline 24.8 & F \\ \hline 26 & M \\ \hline 25.4 & F \\ \hline 26 & M \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline 27 & M \\ \hline 23.5 & F \\ \hline 29 & F \\ \hline \end{array}\)
...