If j is chosen at random from the set {4,5,6} and k is chosen at random from the set {10,11,12}, what is the probability that the product of j and k is divisible by 5?
Answer is 5/9
Tom and Alison are both salespeople. Tom’s weekly compensation consists of $300 plus 20 percent of his sales. Alison’s weekly compensation consists of $200 plus 25 percent of her sales. If they both had the same amount of sales and the same compensation for a particular week, what was that compensation, in dollar?
If the product is to be divisible by 5, either 5 or 10 must be picked. So if 5 is picked for j, then 10, 11, or 12 would work. That’s 3. Then if 10 were to be picked for k, then either 4, 5, or 6 can be picked for j. Since 5,10 is repeated, we subtract 1, giving us 5 possibilities. Total possibilities can be found by multiplying 3x3=9. Therefore, chance is 5/9.
For the second one, it’s impossible for $20 to be the answer, unless you wrote the question wrong. Already, both Tom and Alison have over 20 in compensation because they have $300 and $200 constant.
Slightly different solution for 1. using complementary counting:
P(jk divisible by 5) = 1 - P(jk not divisible by 5)
For jk to not be divisible by 5, we want j = 4 or 6, and k = 11 or 12, giving 2*2 = 4 possibilities (out of 9). So P(jk divisible by 5) = 1 - 4/9 = 5/9.