Question 178104
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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