Math Problems, Probability Problems

Problem of the Day: 1/26/13

A jar contains 4 red marbles & 4 blue marbles. If Shruti removes one marble at a time without replacement, what is the probability that the first 2 marbles she chooses are red?

Solution to yesterday’s problem:

Let’s designate the width of the photograph as x. Then the length of the photograph is x + 2. Since there is a 2-inch border on all sides of the photo, the width of the frame must be x + 4, and the length must be x + 2 + 4, or x + 6. We are given the fact that the area of the total frame is 120 square inches, so we can write an equation like this:


This looks like a factored quadratic equation, but it isn’t because we need zero on the right side. So let’s turn it into a normal quadratic by FOILing (first, outer, inner, last):

x^2+6x+4x+24=120 or x^2+10x+24=120

Now to get zero on the right, all we have to do is subtract 120.


To factor this, we need to find two factors of 96 whose difference is 10. We arrive at 6 and 16. So the factored form of this equation is


This equation is true whenever either of the factors is zero; if x – 6 = 0 or if x + 16 = 0. Solving these two equations gives us x = 6 or x = -16. Obviously the width of the photo cannot be negative, so we know that the width is 6 inches.


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