Question

n a regular deck of 52 cards, there is a .25 probability of randomly selecting a card in the heart suit. Would the experimental probability be higher, lower, or equal to .25?

Answer 1

i think it would be equal to right?

Answer 2

that's what I would think too.

Answer 3

it could be higher/lower or equal

Answer 4

but it SHOULD be equal over enough trials.

Answer 5

it should be close to .25 when a large number of trials is done

Answer 6

is the experiment legitimate /

Answer 7

Are we in Vegas or Atlantic City?

Answer 8

huh?

Answer 9

well if your holding two hearts and there is two on the board, and you just need that last one for the flush of the river, ......
your chances are certainly less than 1/4

Answer 10

for the flush on the river*

Answer 11

true

Answer 12

in a valid experiment ,i.e. shuffled deck, enough samples, i cannot see why you wouldn't get the expectation value

Answer 13

mine was just a bad joke...

Answer 14

what if the theoretical probability is an irrational number. The experimental probability is always a rational number so it will only equal the theoretical probability in the limit

Answer 15

can you give example of a experiment involving a theoretical irrational probability

Answer 16

Good question Unk I wanna know too

Answer 17

Let \[X\] have a continuous uniform distribution.

What is the probability thet X is less than 1/pi

\[\mathbb{P}\left(X<\frac{1}{\pi}\right)\]

Answer 18

yes but what sort of experiment would this formula correspond to?

Answer 19

I should have specified the support...lets use uniform (0,1)

randomly generate a value from a uniform (0,1). That is the experiment

Answer 20

hmmm... is this a computer science type of experiment? I'm not familiar with this terminology "use uniform (0,1)
randomly generate a value from a uniform (0,1)."
This may just be over my head, I've never taken probability or done much computer science, but thank's for the lead, I'll look into it.

Answer 21

cards?

Answer 22

with cards...no...but this statement

"in a valid experiment ,i.e. shuffled deck, enough samples, i cannot see why you wouldn't get the expectation value " is still false

Answer 23

can you explain to me why "?

Answer 24

it sounds like you are saying that if we repeated the experiment enough times we would be guaranteed to have the experimental prob=theoretical prob. is that what you are saying?

Answer 25

if we repeat a valid experiment,yes,

Answer 26

how large would the number trials have to be?

Answer 27

that depends of the uncertainty in the measurement

Answer 28

like you said, they should converge to the theoretical probability as the number of trials approaches infinity

Answer 29

what about for this problem?

Answer 30

that is true...they are equal in the limit, but for any finite number of trials we are not guaranteed to have equality

Answer 31

well then in order to answer the original question we need to know how they defined "experimental probability" as opposed to "theoretical probability"

Answer 32

well if you get to the end of the 52 two cards i bet you'll have 1/4 hearts....
joking.

Answer 33

This conversation is a good example of why we need a new system on openstudy, where people like Zarkon are known as 'people who know what the hell they're talking about'

In practice, over a sample of n draws, the number of times a heart is drawn, h(n), could be more or less or equal to n/4. However is also is true is that
\[\lim_{n \rightarrow \infty} \frac{h(n)}{n} = \frac{1}{4}\]

But that doesn't mean that h(1) = 1/4 (in fact, it can't, as h(.) is integer valued); nor does it mean h(4) = 1 with absolute certainty.

If you're really in any doubt about this. Take a deck of cards, shuffle them thoroughly, pick a card, note its suit, replace the card, reshuffle thoroughly and repeat a few times.

Answer 34

I'm pretty sure JamesJ would fall into that category too.

Answer 35

experiments cannot have absolute certainty . it is a physical impossibility.

going back to measuring experimentally a theoretical irrational numbers. i was hoping you were gonna say something like, Measuring the coastline of a roughly country. The Value determined would be dependent on the size of your measuring stick, as coastlines are not square-edged, a 10 km ruler or a 30 cm ruler would not agree on the coastline as all measuring sticks make approximations around the curves.
With a small measuring stick a larger coastline is measured.
The true coastline length is kinda like a fractal, so i guess the theoretical expectation value would be a function of the ruler

Answer 36

Apparently you are hung up on actually performing the experiment...how about this...make a spinner...like one a child would use for a game. the spinner is broken up into 4 zones. It looks like each are the same size but we know that it is not possible to be that exact...therefore the theoretical probabilities will not be exactly .25 for each zone. there is a chance (I'd say with probability 1) that the regions have a probability that is an irrational number......