Question 1093847: The probability of an event A is 3-4x. Find the value of x which can be and cannot be.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the probability of an event has to be greater than or equal to 0 and less than or equal to 1.
therefore:
3-4x >= 0 and 3-4x <= 1
when 3-4x >= 0, solve for x to get x <= 3/4.
when 3-4x <= 1, solve for x to get x >= 1/2.
x has to be greater than or equal to 1/2 and less than or equal to 3/4.
x cannot be less than 1/2 and cannot be greater than 3/4.
when x = 1/2, 3-4x becomes 3-4*1/2 which becomes 3-2 which becomes 1.
when x = 3/4, 3-4x becomes 3-4*3/4 which becomes 3-3 which becomes 0.
if x is less than 1/2, say 0, then you get 3-4*0 = 3-0 = 3 which is invalid.
if x is greater than 3/4, say 1, then you get 3-4*1 = -1 which is invalid.
when x is between 1/2 and 3/4, say 5/8, then you get 3-4*5/8 = 3-20/8 = (24-20)/8 = 4/8 = 1/2 which is between 0 and 1, therefore valid.
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