What is the product? 3x[-6 -14 -11 -9]
1 answer:
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Answer:
is the required probability.
Step-by-step explanation:
Total number of Marbles = Blue + Red
Probability of getting blue
Probability of not getting a blue
To get exactly one blue in two draws, we either get a blue, not blue, or a not blue, blue.
<u>First Draw Blue, Second Draw Not Blue:</u>
1st Draw:
2nd Draw: (since we did not replace the first marble)
To get the probability of the event, since each draw is independent, we multiply both probabilities.
<u>First Draw Not Blue, Second Draw Not Blue:</u>
1st Draw:
2nd Draw: (since we did not replace the first marble)
To get the probability of the event, since each draw is independent, we multiply both probabilities.
To get the probability of exactly one blue, we add both of the events:
It looks like the integral is
where <em>C</em> is the circle of radius 2 centered at the origin.
You can compute the line integral directly by parameterizing <em>C</em>. Let <em>x</em> = 2 cos(<em>t</em> ) and <em>y</em> = 2 sin(<em>t</em> ), with 0 ≤ <em>t</em> ≤ 2<em>π</em>. Then
Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on <em>C</em> nor in the region bounded by <em>C</em>, so
where <em>D</em> is the interior of <em>C</em>, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: .