Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

1) there is a square in the XY co-ordinate system with its [#permalink]
25 Sep 2003, 06:58

1) there is a square in the XY co-ordinate system with its vertices
as {(1,1), (1,-1), (-1,-1), (-1,1)}. What is the probability that a
point picked at random within this square region will satisfy the
equation x^2+y^2<1?

2) if 2 numbers are chosen from 0-9 inclusive, what is the
probability that its product will be even?

1. Please can u explain how the equation is the origin of a circle. I do not understand.

2. I do not understand why 1-p(O,O) is used, as we need to select only one even number, the second number can be either odd or even, as we nedd the product ot be even.

(1) the equation of an origin-centered circumference is x^2+y^2=R^2, a direct use of the Pythagorean theorem.

(2) all the possible combinations for a product are EE, EO, OE, OO. The first three gives an even product; the last one gives an odd one. So, it is correct to calculate probabilities for each of the first three cases and add them up, but it is more concise and elegant to calculate the probability of the opposite case and subtract it from 1.

1. Because there is no term having x and y in the equation of circle. A general equation of circle is (X-x)**2 + (Y-y)**2=R**2. That's why it's circle having centre as origin and radius is 1.

2. There should be atleast one number should be even out of 2, if there multiplication is even. So if deduct probability of multiplication of (odd,odd) from total probability (i.e. 1), we can get desired probability.