Suppose the data to the right represent Male Female Child Total the survival data for the a certain ship Survived $243 \quad 396$ 79 718 that sank. The males are adult males and the Died 1,099 72 53 1,224 females are adult females. Complete parts (a) Total 1,342 468 132 1,942 through (j).
(t) It a temale passenger is selected at random, what is the probability that she survived?
0.846 (Round to three decimal places as needed.)
(g) If a child passenger is selected at random, what is the probability that the child survived?
(Round to three decimal places as needed.)
Answer
So, the probability that a child passenger survived is \(\boxed{0.598}\).
Step 1 ：Given the data, we are asked to find the probability of survival for a female passenger and a child passenger.
Step 2 ：First, let's calculate the probability for a female passenger. The total number of passengers is 1942, and the total number of females is 468. Out of these, 396 females survived.
Step 3 ：The probability of an event A given that another event B has occurred is given by P(A|B) = P(A ∩ B) / P(B). In this case, event A is survival and event B is being a female.
Step 4 ：We calculate P(A ∩ B) by dividing the number of surviving females by the total number of passengers, which gives us \(\frac{396}{1942} = 0.203913491246138\).
Step 5 ：P(B) is the total number of females divided by the total number of passengers, which gives us \(\frac{468}{1942} = 0.24098867147270855\).
Step 6 ：Using these values, we find that P(A|B) for a female passenger is \(\frac{0.203913491246138}{0.24098867147270855} = 0.846\).
Step 7 ：So, the probability that a female passenger survived is \(\boxed{0.846}\).
Step 8 ：Next, let's calculate the probability for a child passenger. The total number of children is 132, and out of these, 79 children survived.
Step 9 ：We calculate P(A ∩ B) by dividing the number of surviving children by the total number of passengers, which gives us \(\frac{79}{1942} = 0.040679711637487126\).
Step 10 ：P(B) is the total number of children divided by the total number of passengers, which gives us \(\frac{132}{1942} = 0.06797116374871266\).
Step 11 ：Using these values, we find that P(A|B) for a child passenger is \(\frac{0.040679711637487126}{0.06797116374871266} = 0.598\).
Step 12 ：So, the probability that a child passenger survived is \(\boxed{0.598}\).
