Question

Probability: A hospital administrator codes incoming patients suffering gunshot wounds according to whether they have insurance (coding 1 if they do and 0 if they do not) and according to their condition, which is rated as good (g), fair (f), or serious (s). Consider and experiment that consists of the coding of such a patient.
(a) Give the sample space of this experiment.
(b) Let A be the event tat the patient is in serious condition. Specify the outcomes in A.
(c) Let B be the event that the patient is uninsured. Specify the outcomes of B.
(d) Give all the outcomes in the event B^c U A

Answer 1

Insurance : 0, 1
Condition : g, f, s

Answer 2

Im not sure i understand what the sample space is

Answer 3

sample space is just a set of `all possible outcomes`

Answer 4

i see

Answer 5

(0, g), (0, f), (0, s)

(1, g), (1, f), (1, s)

Answer 6

they are the all possible outcomes in sample space^

Answer 7

so 2/6 of the time the patients are in a serious condition?

Answer 8

the first index specifies the `Insurance`
and the second index specifies the `Condition`

Answer 9

Exactly ! but thats not what part b is asking us to find

Answer 10

part b is asking us to directly list down the outcomes

Answer 11

what are the outcomes that have `s` ?

Answer 12

(0,s) (1,s)

Answer 13

Correct !

Answer 14

thats all? haha I'm way overthinking this

Answer 15

thats all for part b :)

Answer 16

so part c would be (1,g), (1,f), (1,s)

Answer 17

careful :

0 = uninsired
1 = insured

Answer 18

oops, yes (0,g) (0,f) (0,s)

Answer 19

looks good

Answer 20

so i think it wants me to put it in a set B? how would that look? B:(0,g)....

Answer 21

or P(B)?

Answer 22

which part

Answer 23

well as i get the answers of part b and c, i come to d and it is referencing to the previous parts (perfectly normal) but it is labeling them as A and B. I want to get the notation right so, would proper notation for part c be P(B) = (0,g), (0,f), (0,s). ?

Answer 24

and then how would i finish part d, haha

Answer 25

good :) we're not doing any probability stuff here so we should not use P(B) etc..

Answer 26

we need to use the set notation instead

Answer 27

Part a :
U = {(0, g), (0, f), (0, s), (1, g), (1, f), (1, s)}

Part b :
A = {(0,s) (1,s)}

Part c :
B = {(0,g), (0,f), (0,s)}

Answer 28

perfect! thanks that looks like the correct answer haha

Answer 29

so B compliment U A would be everything not in B set and everything inside set A.. are duplicates allowed?

Answer 30

:) for part d you need to know a small new notation

Answer 31

you're right !! duplicates are not allowed

Answer 32

heyyyy, you're a good teacher, haha

Answer 33

so i got B^c U A = { (1,g), (1,f), 1,s), (0,s)}

Answer 34

Looks perfect ! no, you're supersmart lol good job :)