Question

You are literally trying to find a needle in a haystack. There is a needle hidden somewhere in a bale
of hay, which is in the shape of a cube, 3 feet to a side. If the needle is equally likely to be anywhere
in the haystack, what is the probability the eye of the needle is more than 0.5 feet from the centre and
more than 1 foot from the bottom right front corner of the haystack?

Answer 1

The probability that the eye of the needle is more than 0.5 feet from the centre is computed here as:

= (Probability that the eye of the needle is more than 0.5 feet away from the centre and more than 1 foot from the bottom right front corner of the haystack) / Total volume of the cube

= ( Volume of of cube - Volume of sphere at the centre with radius 0.5 feet - Volume of quarter sphere at the bottom right corner ) / Total volume of the cube

Therefore 0.9418 is the required probability here.