The organized list below shows all possible outcomes when four fair coins are flipped.
Each coin lands facing either heads up (H) or tails up (T).

HHHT HTHH HHTT HHTH HTHT HTTH HTTT

TTTH THTT TTHH TTHT THTH THHT THHH

What is the probability that at least three coins land facing tails up? Give the probability as a percent.

The probability that at least three coins land facing tails up is 4 and in percentage term we can write it as .25%

Step-by-step explanation:

Step 1

Let H = Heads, T = Tails

Each of the 4 tosses can be either H or T, so there are 4^2= (16) possibilities/Probabilities

Step 2:

The 16 possibilities/probabilities  are:

4 H,

3 H and 1 T (in various orders),

2 H and 2 T (in various orders),

1 H and 3 T (in various orders), or 4 T.

Step 3

The more detailed information needed is mentioned below

The probability of getting  4 Heads

4 H = H H H H

The probability of getting 3 Head and 1 Tail (arranged in various orders)

3 H and 1 T: H H H T, H H T H, H T H H, T H H H

The probability of getting 2 Head and 2 Tail (arranged in various orders)

2 H and 2 T: H H T T, H T T H, T T H H, H T H T, T H T H, T H H T

The probability of getting  1 Head and 3 Tail (arranged in in various orders)

1 H 3 T: H T T T, T H T T, T T H T, T T T H

The probability of getting  4 Tail

4 T: T T T T

So we can say that the probability of getting is 4 or .25%(4/16)

1 Head and 3 Tail (arranged in in various orders)

H T T T, T H T T, T T H T, T T T H

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.