Naomi is still not sure how many boxes of each type of candy to order. Her dad explains that he needs to do a little more mathem
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We find the probability of intersection using the inclusion/exclusion principle:
By definition of conditional probability,
For
in which case we have
Or, to establish independence another way, in terms of conditional probability, we must have
which is also true.
Its not clearly given that whether EBF = 2x + 9 or 2x - 9.
I have written the solution for both.
If EBF = 2x + 9,
then ABF = 6x + 26 and ABE = 11x - 31.
Now, ABE = ABF + EBF
11x - 31 = (6x + 26) + (2x + 9)
= (6x + 2x) + (26 + 9)
= 8x + 35
11x - 8x = 35 + 31
3x = 66
x = 22
Therefore, ABF = 6x + 26 = 6(22) + 26 = 132 + 26 = 158°
If EBF = 2x - 9,
then ABF = 6x + 26 and ABE = 11x - 31.
Now, ABE = ABF + EBF
11x - 31 = (6x + 26) + (2x - 9)
= (6x + 2x) + (26 - 9)
= 8x + 17
11x - 8x = 17 + 31
3x = 48
x = 16
Therefore, ABF = 6x + 26 = 6(16) + 26 = 96 + 26 = 122°
