Guys i have this probability problem and i wanted to know if you can help me with it:
Suppose the weatherman estimates the probability of rain tomorrow as 60%, the probability of lightning as 50%, and the probability of both rain and lightning as 20%. We determine the probability that tomorrow there will be
a) no rain,
b) no lightning,
c) rain or lightning,
d) rain but no lightning,
e) lightning but no rain,
f) neither rain nor lightning.
I guess over 50% means it happens?
There's 4 possibilities:
(1) It only rains.
(2) There's only lightning.
(3) There is both rain and lightning.
(4) There is neither rain nor lightning.
When they say 60% chance of rain, that means regardless of the other stuff that happens. So which categories have rain up there? (1) and (3).
When they say 50% chance of lightning, that means regardless of the other stuff that happens. So which categories have lightning up there? (2) and (3).
When they say 20% chance of both rain and lightning, they refer to (3).
So you need to know the chances of each thing happening.
If you want just (1) then you take (1)+(3) - (3) which is 60% - 20% = 40%.
If you want just (2) then you take (2)+(3) - (3) which is 50% - 20% = 30%.
If you want just (3) then you take (3) which is 20%.
If you want just (4) then you take 100% - (1) - (2) - (3) = 10%.
So there's a 40% chance of just rain, 30% chance of just lightning, 20% chance of both, and a 10% chance of neither.
Choices (a) and (b) say no rain and no lightning. For the former you want 100% - (1) - (3) = 40%. For the latter you want 100% - (2) - (3) = 50%.
Choice (c) wants rain OR lightning. That means any case that has one or the other. Or, it means 100% - (4). Either way, you get 90%.
(a) is 40%
(b) is 50%
(c) is 90%
(d) is 40%
(e) is 30%
(f) is 10%
I'd go with (c). Rain or lightning.
