## INT 3 years ago There is a 0.63 probability that Mobil stock will rise, a 0.75 probability Gulf stock will rise and a 0.4 chance that both stocks will rise. Find the probability that neither stock will rise. There is a 0.63 probability that Mobil stock will rise, a 0.75 probability Gulf stock will rise and a 0.4 chance that both stocks will rise. Find the probability that neither stock will rise. @Mathematics

1. INT

So .37*.25=.0925 But the answer key for a similar problem( only difference is .47 instead of .4), the answer is .2775. The answers shouldnt differ that much right?

2. Zarkon

why are you multiplying those two numbers?

3. INT

isnt that how you get the probability for AND?

4. Zarkon

not in this case

5. INT

Then Im completely lost.

6. Zarkon

your events are NOT independent

7. INT

I think that's the concept that I dont quite understand

8. INT

would the formula be P(A U B)/P(A)?

9. Zarkon

no

10. Zarkon

use \[P(A^c\cap B^c)=1-P(A\cup B)\]

11. INT

so the 1-P(none) formula

12. Zarkon

for any event E \[P(E)=1-P(E^c)\] or \[P(E^c)=1-P(E)\]

13. INT

so how exactly does not being independent effect the problem?

14. Zarkon

events A and B are independent iff \[P(A\cap B)=P(A)P(B)\]

15. Zarkon

you cant use this formula since A and B are not independent

16. INT

So in terms of a venn diagram, independent is two circles that dont intersect. and not independent has two circles that do intersect. and in this problem the intersection is .4? So I need to find the sum of each part of the venn diagram, subtract from one (to get the number outside the diagram) which would be the "neither". Correct?

17. Zarkon

NO

18. Zarkon

independent events intersect (most of the time)

19. Zarkon

if A and B are independent and P(A)>0 and P(B)>0 then A and B have to intersect.

20. Zarkon

use \[P(A^c\cap B^c)=1-P(A\cup B)=1-[P(A)+P(B)-P(A\cap B)]\]

21. INT

|dw:1321204843404:dw| Is what Im picturing Basically, I was doing P(Ac∩Bc)=1−P(A∪B)=1−[P(A)+P(B)−P(A∩B)] except that mine adds instead of subtracts the intersection.

22. INT

so to get neither dont you need to get rid of all that is in the circles? including the intersection?

23. Zarkon

yes

24. INT

wouldnt that be adding the intersection? so 1−[P(A)+P(B)+P(A∩B)] instead of 1−[P(A)+P(B)−P(A∩B)]

25. INT

oh wait

26. INT

I see nevermind

27. INT

|dw:1321205205257:dw| So the answer is .02? that's seems really small.(compared to the other answer)

28. Zarkon

it is .02

29. INT

ok thanks

30. Zarkon

I would check your key again...if you just change from .4 to .47 then .2775 is not the answer