Three points are selected at random on a sphere's surface. What is the probability that they all lie in the same hemisphere?
Assume that the great circle, bordering a hemisphere, is part of the hemisphere.
No matter how we place the points on a sphere it will without any doubt fall in one of the infinite possible hemispheres that can be chosen.
So the asked probability is 1 ie., 100%.
In space, the three points define a plane cutting the sphere in two pieces. The smaller of these two spherical caps is always contained in half of a sphere: a hemisphere.
Thus the answer is: 100% probable.
There are 12 boys and 9 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?
I have a stick of length 3 cm and I select 2 random points on it and break it at those points to get 3 pieces.
If the probability that these pieces will form a triangle is m/n where m and n are coprime integers then what is the value of m × n?
Two digits are selected at random from digits 1 through 9. If sum is even, find the probability that both numbers are odd?
There are 8 boys and 5 girls in a class. If four students are selected at random, what is the probability that 2 girls and 2 boy are selected?
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