## Pulsified333 one year ago about events A and B of a sample space S, but assume that Pr[A′]=0.3, Pr[B]=0.5, and Pr[A′∩B]=0.2. Find the probabilities of the following events: (1) Pr[A∩B]= (2) Pr[A∪B]= (1) Pr[A′∪B]=

1. Pulsified333

@dan815

2. anonymous

|dw:1442540376873:dw|

3. anonymous

do you know where \(A'\cap B\) is in the picture ?

4. Pulsified333

B

5. anonymous

shade it in not B, but \(A'\cap B\)

6. Pulsified333

then what is A′∩B

7. anonymous

the stuff in B that is not in A

8. Pulsified333

|dw:1442540600013:dw|

9. anonymous

got it now lets put a \(0.2\) there |dw:1442540629245:dw|

10. Pulsified333

so that mean A U B is .3

11. anonymous

what you really mean is \[P(A\cap B)=0.3\] and the answer is yes

12. Pulsified333

13. anonymous

|dw:1442540747197:dw|

14. Pulsified333

then how does A' is .3

15. anonymous

the .2 is in \(A'\) cause it is not in A also the stuff outside of both in in A' you used up .2 in B, that leaves only .1 outside

16. anonymous

|dw:1442540852342:dw|

17. Pulsified333

so A = .4

18. anonymous

now all that is left to do is figure out what goes in \(A\cap B'\) the missing part all this has to add up to 1, so make sure it does

19. anonymous

yeah right

20. anonymous

|dw:1442540918987:dw|

21. anonymous

now you can figure out any probability you like from the picture, so long as you know what the set is