Question

Find the indicated probabilities for the experiment described in the previous problem: 19. PJ AB) 21. P( BS) 23. P(JUS) The following contingency table contains the counts of those who did and did not survive the sinking of the RMS Titanic, along with whether they were adults or children. Find the following probabilities: Child Adult Total Did not survive 52 1438 1490 Survived 57 654 711

Answer 1

solution:

the given contingency table is as follows:

	child	adult	total
Did not survive	52	1438	1490
survived	57	654	711
total	109	2092	2201

25) P(child or adult) = P(child) + P(adult)

both events are mutually exclusive so there is no P(child and adult)

there are total 109 child out of total person 2201

so P(child) = 109 / 2201

there are 2092 adult out of total 2201

P(adult) = 2092 / 2201

P(child or adult) = (109/2201) + (2092 / 2201) = 2201/2201 = 1

27) P(child and survived)

there are 57 child and who are survived also out of total 2201 person

so, P(child and survived) = 57 / 2201 = 0.0259

33)

P(adult or survived) = P(adult) + P(survived) - P(adult and survived)

P(Adult) = 2092 / 2201..............there are 2092 adult out of total 2201 person.

P(survived) = 711 / 2201.................there are 711 survived person out of 2201 person.

P(adult and survived) = 654 / 2201.........654 are counted twice in both the event who are adult survived

P(adult or survived) = $\frac{2092}{2201}+\frac{711}{2201}-\frac{654}{2201}= \frac{2149}{2201}=0.9764$

35)

P(adult or did not survived) = P(adult) + P(did not survived) - P(adult and did not survived)

P(Adult) = 2092 / 2201

P(did not survived) = 1490/ 2201

P(adult and did not survived) = 1438 / 2201

P(adult or did not survived) = $\frac{2092}{2201}+\frac{1490}{2201}-\frac{1438}{2201}= \frac{2144}{2201}=0.9741$