What is the probability of an event that is impossible? suppose that a probability is approximated to be zero based on empirical results. does this mean that the event is impossible?

Explanation:

For the first question, the mathematical (statistical, to be more precise) definition of a event that is impossible is that its probability is zero.

There are two extremes when you talk about probability: 0 and 1. 0 means that the event cannot occur in any way, while 1 is that the event is certain (it cannot not happen).

An example of an event with probability 0 is: men born in the Sun. This is an impossible event, and so there is no chance (probability 0) to find a man born in the Sun.

For the second question, when you deal with empirical results, this is with an experiment, the fact of having a probability zero as result of approximations does not make that an event be impossible; the event is unlikely (if the experiments were carried out properly) but yet it can happen.

For example, say you put 1,000 ballots in a bag with the number 3, together with 1 ballot with the number 9. Then, you perform the experiment of drawing a ballot 2,000 times. Suppose you draw the ballot with the number 9 two times. In that case, your approximated experimental probability of drawing a 9 will be 2 /2,000 = 0.001. Which you could round to 0.00. That may be valid but it cannot be taken as that the event of drawing the ballot with the number 9 is impossible, it is just unlikely.

you divide the cost ($15) by the quantity (6) to get your questions answer. the yo-yo costs $2.50. hope this : )!

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.