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.&nbsp;Class&nbsp;Survived&nbsp;&nbsp;&nbsp;First&nbsp;&nbsp;Second&nbsp;&nbsp;Third&nbsp;&nbsp;Yes&nbsp;19794151&nbsp;No&nbsp;122167476&nbsp;&nbsp;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).

Question

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.&amp;nbsp;Class&amp;nbsp;Survived&amp;nbsp;&amp;nbsp;&amp;nbsp;First&amp;nbsp;&amp;nbsp;Second&amp;nbsp;&amp;nbsp;Third&amp;nbsp;&amp;nbsp;Yes&amp;nbsp;19794151&amp;nbsp;No&amp;nbsp;122167476&amp;nbsp;&amp;nbsp;Let&#039;s say we choose at random one of the Titanic&#039;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).

nitruraviX · Accepted Answer

DEFINITIONS  Complement rule:  P(Ac)=P(not A)=1−P(A)  Definition conditional probability:  P(B|A)=P(A∩BP(A)=P(A and B)P(A)  SOLUTION  Given:   First  Second  Third TotalSurvived19794151442Not survived 122167476765Total3192616271207  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)=# of favorable outcomes# of possible outcomes=3191207  Complement rule:  P(not A)=1−P(A)  Using the complement rule, we then obtain: P(FC)=1−P(F)=1−3191207=8881207  442 of the 1207 people on the Titanic survived.  P(DC)=# of favorable outcomes# of possible outcomes=4421207  94+151=245 of the 1207 people on the Titanic were not a passenger in first class and survived.  P(FC and Dc)=# of favorable outcomes# of possible outcomes=2451207  Use the general addition rule:  P(FC and Dc)=P(Fc)+P(Dc)−P(Fc and Dc)=8881207+4421207−2451207=888+442−2451207=10851207≈0.8989=89.89%  Result:  10851207≈0.8989=89.89%

Ian Adams · Accepted Answer

Given:  FirstSecondThirdTotalSurvived19794151442Not survived122167476765Total3192616271207 94+151=245 of the 1207 people on the Titanic were not a passenger in first class and survived. The probability is the number of favorable outromes divided by the number of possible outromes: P(FCandDc)=# of favorable outromes/# of possible outromes=2451207∼−0.2030=20.30%