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?