statistic

stan56

basically i'm looking for formulae in probablilty or how do you claculate probability. there is an event which occurs say y times , the probability of it being true is say X how do you calculate if its going to be true at least A times, at most A times or exactly A times. ( I am using letters rather than figures so that i can apply it to a number of questions in a past paper)
any help appreciated

king_of_inismac

say you flip a coin 100 times and the probability of it being heads in 50% (pedants ignore any bias in the coin!)

You can't calculate how MANY times its going to be true at least A times, at most A times or exactly A times

You can calculate whats the PROBABILITY its going to be true
at least A times, at most A times or exactly A times

stan56

king_of_inismac wrote: »

say you flip a coin 100 times and the probability of it being heads in 50% (pedants ignore any bias in the coin!)

You can't calculate how MANY times its going to be true at least A times, at most A times or exactly A times

You can calculate whats the PROBABILITY its going to be true
at least A times, at most A times or exactly A times

sorry, ya i meant the probability

king_of_inismac

From what I remember (I dont use probability in my line of work)
say I flip a coin 10 times:

At least three heads:
(1/2)*(1/2)*(1/2). The rest we don't care about the rest

At most three times (head)
You can rephrase it as at least 7 tails, so the same method as above
(1/2)*(1/2)*(1/2)*(1/2)*(1/2)*(1/2)*(1/2)

hivizman

This is an example of the binomial distribution. It applies when you have a number of identical and independent events (such as tossing a coin) with two possible but mutually exclusive outcomes (e.g. heads or tails).

Suppose that the probability of one outcome is p, then the probability of the other outcome is (1-p) (given two possible outcomes, one and only one of which can occur, the probabilities must sum to 1).

If you want the probability that, out of n events, you get the selected outcome exactly r times, this is given by the formula:

p^r x (1-p)^(n-r) x (n!/(r! x (n-r)!))

[r! = 1 x 2 x 3 x . . . x (r-1) x r]

Where the two possible outcomes are equally probable (e.g. tossing a fair coin), p = 1/2, so 1-p = 1/2, and the formula simplifies to:

(1/2^n) x (n!/(r! x (n-r)!))

For 10 coins, the probabilities of 0, 1, 2 etc heads are:

number....probability of....... probability of
of heads..exactly r heads.... r heads or less

0.......... 0.000976563....... 0.000976563
1.......... 0.009765625....... 0.010742188
2.......... 0.043945313....... 0.0546875
3.......... 0.117187500....... 0.171875
4.......... 0.205078125....... 0.376953125
5.......... 0.246093750....... 0.623046875
6.......... 0.205078125....... 0.828125
7.......... 0.117187500....... 0.9453125
8.......... 0.043945313....... 0.989257813
9.......... 0.009765625....... 0.999023438
10........ 0.000976563....... 1

So the probability of at least 3 heads is 1 minus the probability of two heads or less, that is 1 - 0.0546875 = 0.9453125.