ossidianaZ

Answered

2021-02-12

On its first journey, the Titanic was struck by an iceberg in 1912 and sank. Some passengers used the lifeboats to leave the ship, but many perished. By class of travel, the following two-way table lists the adult passengers who perished and those who survived.

$\begin{array}{lcc}& \text{Class}\text{}\text{Survived}& \begin{array}{cccc}& \text{First}& \text{Second}& \text{Third}\\ \text{Yes}& 197& 94& 151\\ \text{No}& 122& 167& 476\end{array}\text{}\end{array}$

Let's say we choose at random one of the Titanic's adult passengers. Give event D the definition of receiving a death, and event F the definition of receiving a first-class passenger. Find P (not a passenger in first class or survived).

Answer & Explanation

nitruraviX

Expert

2021-02-13Added 101 answers

DEFINITIONS

Complement rule:

$P({A}^{c})=P(not\text{}A)=1-P(A)$

Definition conditional probability:

$P(B|A)=\frac{P(A\cap B}{P(A)}=\frac{P(A\text{}and\text{}B)}{P(A)}$

SOLUTION

Given:

$\begin{array}{lcccc}& \text{First}& \text{Second}& \text{Third}& \text{Total}\\ \text{Survived}& 197& 94& 151& 442\\ \text{Not survived}& 122& 167& 476& 765\\ \text{Total}& 319& 261& 627& 1207\end{array}$

319 of the 1207 people on the Titanic were a passenger in first class.

The probabillity is the number of favorable outcomes divided by the number of possible outcomes:

$P(F)=\frac{\text{\# of favorable outcomes}}{\text{\# of possible outcomes}}=\frac{319}{1207}$

Complement rule:

$P(not\text{}A)=1-P(A)$

Using the complement rule, we then obtain:$P({F}^{C})=1-P(F)=1-\frac{319}{1207}=\frac{888}{1207}$

442 of the 1207 people on the Titanic survived.

$P({D}^{C})=\frac{\text{\# of favorable outcomes}}{\text{\# of possible outcomes}}=\frac{442}{1207}$

94+151=245 of the 1207 people on the Titanic were not a passenger in first class and survived.

$P({F}^{C}\text{}and\text{}{D}^{c})=\frac{\text{\# of favorable outcomes}}{\text{\# of possible outcomes}}=\frac{245}{1207}$

Use the general addition rule:

$P({F}^{C}\text{}and\text{}{D}^{c})=P({F}^{c})+P({D}^{c})-P({F}^{c}\text{}and\text{}{D}^{c})\phantom{\rule{0ex}{0ex}}=\frac{888}{1207}+\frac{442}{1207}-\frac{245}{1207}\phantom{\rule{0ex}{0ex}}=\frac{888+442-245}{1207}\phantom{\rule{0ex}{0ex}}=\frac{1085}{1207}\phantom{\rule{0ex}{0ex}}\approx 0.8989\phantom{\rule{0ex}{0ex}}=89.89\mathrm{\%}$

Result:

$\frac{1085}{1207}\approx 0.8989=89.89\mathrm{\%}$

Complement rule:

Definition conditional probability:

SOLUTION

Given:

319 of the 1207 people on the Titanic were a passenger in first class.

The probabillity is the number of favorable outcomes divided by the number of possible outcomes:

Complement rule:

Using the complement rule, we then obtain:

442 of the 1207 people on the Titanic survived.

94+151=245 of the 1207 people on the Titanic were not a passenger in first class and survived.

Use the general addition rule:

Result:

Ian Adams

Expert

2021-08-12Added 160 answers

Given:

The probability is the number of favorable outromes divided by the number of possible outromes:

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