Mia surveyed the students at her school to find out if they like the color black and/or pink. The results of her survey are show
n in the two-way table below:
If a student does not like pink, what is the probability that student also does not like black?
18.0%
21.9%
28.1%
39.1%
If a student does not like pink, what is the probability that student also does not like black?
18.0%
21.9%
28.1%
39.1%
2 answers:
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Given
we have
Squaring both sides, we have
And finally
Note that, when we square both sides, we have to assume that
because we're assuming that this fraction equals a square root, which is positive.
So, if that fraction is positive you'll actually have roots: choose
and you'll have
Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose
and you'll have
Squaring both sides (and here's the mistake!!) you'd have
which is not a solution for the equation, if we plug it in we have
Which is clearly false
