I'll do problem 1 to get you started.
set A = multiples of 3 between 5 and 25 = {6, 9, 12, 15, 18, 21, 24}
there are 7 items in set A, so we can say n(A) = 7
set B = multiples of 5 between 5 and 25 = {5,10,15,20,25}
Here we have n(B) = 5
set C = multiples of 3 and 5, between 5 and 25 = {15}
n(C) = 1 which we can rewrite as n(A and B) = 1.
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To summarize so far,
- n(A) = 7
- n(B) = 5
- n(A and B) = 1
From those three facts, then we can say,
n(A or B) = n(A) + n(B) - n(A and B)
n(A or B) = 7 + 5 - 1
n(A or B) = 11
There are 11 values between 5 and 25 that are multiples of 5, multiples of 3, or both.
Those 11 values are: {5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25}
This is out of 25-5+1 = 21 values overall which are in the set {5,6,7,...,24,25}
So we have 11 values we want out of 21 overall, which leads to the probability 11/21
Final Answer: 11/21
