Math Is Fun Forum

Hi there

I was watching the NZ election live the other night and wondered how confident I could be of knowing the final result given that only 1% of the votes had been counted.

Here is a simplified example

Suppose there are two parties, Party A and Party B

For a party to win the election, they must get more than 50% of votes

1,200,000 votes have been made but only 12,000 have been counted (1%)

Of those counted, Party A has received 7800 votes (65%) and Party B has received 4200 votes (35%)

What is the probability that Party A will win the election?

I appreciate any help or suggestions as to which theorem/s could help me

Thanks

I think it's fairly intuitive that the answer is 11 here, but I'm wondering if there is a more concrete/elegant way of solving this?

Thanks

Hi all

A coin is tossed 150 times

We know that there are only two possible outcomes, heads or tails, however, we don't know what the probability of each result occurring is.

Results:
80 times, it lands on heads
70 times, it lands on tails

What is the probability that heads has a greater than 50% chance of occurring on the next toss?

Any help is appreciated

Find all pairs of real numbers (a,b) such that a/b + b/a >= 2

Any help appreciated

Thanks

Imagine there is a field of infinite daisy chains.

The probability that a given chain contains n daisies is given by the following.

P = 2 / (3^n)

What is the average length of the daisy chains in the field?

Thank you.

Convert

F(x,y,z) = k / (x^2 + y^2 + z^2)^2

into spherical coordinates.

Thanks for the help.

My answer is <0>, <12>, <20>, <32>
Is this correct?

For which values of Z do the following series absolutely converge?

     
  ∑ (Z+1)^n / 2^n

The sum is from n=0 to infinity.

Thanks for any help.

Show that,

|1 − zw*|^2   −   |z − w|^2 = (1 − |z|^2)(1 − |w|^2)

where z and w are complex numbers and z* is the conjugate of z.

Not very fluent with algebraic properties of these things so please help!!
Thanks.

Suppose that f is continuous on the closed interval [a, b], a < b, and that f(a) =
A, f(b) = B, A < B.
Suppose further that f is strictly increasing on [a, b] (i.e. for any x1, x2 ∈ I, x1 <
x2, impliesf(x1) < f(x2)).
Let C be a number between A and B. Show that there is exactly one value of x in
(a, b) such that f(x) = C.

I used the bisection process to try to explain why this must be the case but i'm not convinced that's what they're looking for....any ideas???

For any real number c and any set S ∈ R, we define c + S to be the set {c + x : x ∈ S}.
Prove:
If a set S ⊆ R, and c is any real number, the c + S has a supremum and
sup(c + S) = c + sup S.

Any help is much appreciated, thanks.