# Tutor profile: Carrie L.

## Questions

### Subject: SAT II Mathematics Level 2

There are two boxes of grean cards and red cards. The probability of taking out a red card from Box 1 is p, the probability of taking out a red card from Box 2 is q. We are going to take out one cards from each box. What is the probability that at least one red cards is taken out?

There are totally 4 cases: GG(take out one green card from box 1, and one green card from box 2),GR,RG,RR. The probability that no red cars are taken is equal to the sum of probability of cases (GR,RG, RR), which is (1-p)q + (p)(1-q) + pq; or the other way to solve this problem is 1 - the probability that both cards are green, which is 1 - (1-p)(1-q).

### Subject: SAT II Mathematics Level 1

If (x-3) is a factor of x^3 - 4x + k, what is the value of the constant k?

Since we know (x-3) is a factor of the polynomial function f(x) = x^3 - 4x +k, we know that (f3) = 0 by the factor theorem. Thus we can plug in f(3) = 0 to find k, k = -15.

### Subject: Basic Math

If it takes $10 dollars to buy 2 bags of apples, how much does it cost for each bag of apple?

For questions that ask how much/many item x for each/ per item y, we would like to use the among for item x divided by the corresponding item y. So the answer should be $10/2bags = $5/bag.

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