Question 178104: Please help me with the following question. I have been trying to figure it out, but am having some difficulty.
Is this statement true or false? For any two events, the probability that one or the other of the events occurs equals the sum of the two individual probabilities.
How do you go about figuring this out?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! suppose you have a box with 4 balls in it.
there's a red ball, a green ball, a white ball, and a blue ball.
the probability of getting a red ball is 1/4 since 1 out of the 4 balls will provide you with success.
the probability of getting a blue ball is 1/4 since 1 out of the 4 balls will provide you with success.
the probability of getting a red ball or a blue ball is 2/4 since 2 out of the 4 balls will now provide you with success. it's either a red, or a blue.
this is the same as p(red) + p(blue) = 1/4 + 1/4.
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look at another example:
suppose you had 3 red balls, 5 green balls, 7 white balls, and 15 blue balls.
total universe is now 3 + 5 + 7 + 15 = 30
p(red) = 3/30
p(blue) = 15/30
p(red or blue) = (3+15)/30 = 18/30
why?
if you want to get a red, you only have 3 to pick from.
if you want to get a blue, you only have 15 to pick from.
if you want to get a red or a blue, you have 18 to pick from.
this is the sum of the red and the blue balls.
that's why p(a or b) = p(a) + p(b)
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now p(a or b) = (3 + 15)/30 = 3/30 + 15/30 which is the same as p(a) + p(b)
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