1) there is a square in the XY co-ordinate system with its

Question

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?

stolyar · Answer

(1) X^2+Y^2<1 is an origin-center circle, its radius being 1.

So, employ the geometrical sense of the probability: the favorable area/the total area

FA=pi
TA=4

P=pi/4

(2) P(an even product of the two)=1-P(odd,odd)=1- =1-2/9=7/9

guy123 · Answer

i agree with stolyar

watchdog · Answer

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.

so P(even #)=5/10 * P(any other #)9/9 = 0.5

am i right ?

stolyar · Answer

(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.

smarty_cry · Answer

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.

Vicky · Answer

stolyar's answers are correct.. good.
 -vicky

watchdog · Answer

Thanks for the explanations.

1) there is a square in the XY co-ordinate system with its

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