View Full Version : Math problem

wantafanta

07-05-06, 02:18

I have a nickel in my hand.

If I flip the coin once, the odds that it will land heads up is 50/50.

If I flip the coin again, the odds that it will land heads up is 50/50.

What are the odds of it landing heads up at least once after 2 tries?

tlr online

07-05-06, 02:19

50/50.

wantafanta

07-05-06, 02:23

I don't think that's right. I'm not sure of the correct answer myself. But it has to be better than 50/50 because heads has a greater chance of turning up after 2 flips than after only one!

tlr online

07-05-06, 02:25

If you tossed the coin 9 times, and it fell on tails each time, the chance of it falling on heads on the 10th would still be 50/50.

But Tails has a better chance of turning up too, so doesn't it balance out? :confused:

tlr online

07-05-06, 02:27

OK. Hold on.... thinking.

tlr online

07-05-06, 02:29

OK. You could argue the odds are 75%, because in effect you are reducing the odds by throwing the coin twice. Where 50/50 is the first toss, because you are trying to achieve a pre-defined result (i.e. heads) then you could say the odds increase incrementally by 25%.

But I'm still going with my initial 50/50.

wantafanta

07-05-06, 02:30

The more flips, the greater chance of a head turning up. Think of it like this. If you shake hands with just one person, you might catch a cold. But if you shake hands with a thousand people, you are almost certain to get sick! Likewise, if you flipped a coin 1000 times, it is almost certain to turn heads up at least once.

meansizzler

07-05-06, 02:30

Hmm..A Level Statistics, i'm guessing 25%,

xMiSsCrOfTx

07-05-06, 02:31

I've heard this before somewhere... Isn't the answer like, 49.99999999% or something like that?

tlr online

07-05-06, 02:32

The more flips, the greater chance of a head turning up. Think of it like this. If you shake hands with just one person, you might catch a cold. But if you shake hands with a thousand people, you are almost certain to get sick! Likewise, if you flipped a coin 1000 times, it is almost certain to turn heads up at least once.

I see your point, but I don't agree. It's still a game of chance, and you can't associate better odds with frequency. It's still a 50/50 chance. The odds don't increase in one direction's favour the more you toss.

I have a nickel in my hand.

If I flip the coin once, the odds that it will land heads up is 50/50.

If I flip the coin again, the odds that it will land heads up is 50/50.

What are the odds of it landing heads up at least once after 2 tries?

[Toss1][Toss2]

[H][H] - Event 1

[H][T] - Event 2

[T][H] - Event 3

[T][T] - Event 4

There are 4 events (or outcomes). Heads appears at least once in 3 of the events. Therefore, the odds are 3/4.

Lost_Raider

07-05-06, 02:33

Hum...I'm doing this the dumb way since I can't remember the formula at the moment...

After flipping the coin two times, you will get:

HT

HH

TH

TT

At least one head after two tries...3/4 is 75%

tlr online

07-05-06, 02:35

[Toss1][Toss2]

[H][H] - Event 1

[H][T] - Event 2

[T][H] - Event 3

[T][T] - Event 4

There are 4 events (or outcomes). Heads appears at least once in 3 of the events. Therefore, the odds are 3/4.

Nice :tmb:

Welcome aboard. :)

xMiSsCrOfTx

07-05-06, 02:35

Or at least one head after two tries... 1/2? :confused: That still would make it a 50/50 chance, like tlr said.

meansizzler

07-05-06, 02:36

Hum...I'm doing this the dumb way since I can't remember the formula at the moment...

After flipping the coin two times, you will get:

HT

HH

TH

TT

At least one head after two tries...3/4 is 75%

The boys got it, good job.....

Lost_Raider

07-05-06, 02:39

The boys got it, good job.....

It is rather embrassing that I forgot the formula...I'm studying in this area right now...

meansizzler

07-05-06, 02:40

It is rather embrassing that I forgot the formula...I'm studying in this area right now...

I know I done it ike two years ago, A.B A-B, all that and/or can be really confusing...

wantafanta

07-05-06, 02:42

I think 75% is the correct answer. The odds are 50/50 for any one flip. But the odds improve if you allow more than one flip.

Weirdly, the chances of any 2 students sharing the same birthday in a classroom of 30 are better than 50/50.

CerebralAssassin

07-05-06, 10:50

Hum...I'm doing this the dumb way since I can't remember the formula at the moment...

After flipping the coin two times, you will get:

HT

HH

TH

TT

At least one head after two tries...3/4 is 75%

:tmb: you're correct since all these outcomes have the same probability of happening then you just use the standard formula P(A)=N(A)/N(S).

tha_mattster

07-05-06, 10:54

I dont believe that! I think the probability is always 50%. Each coin flip is a new event, its not like cutting at a rope, each cut making it more likely to snap. How can a previously flip affect the next?

CerebralAssassin

07-05-06, 10:57

I dont believe that! I think the probability is always 50%. Each coin flip is a new event, its not like cutting at a rope, each cut making it more likely to snap. How can a previously flip affect the next?

he's asking what are the probabilities of the coin landing heads up at least once, not once:D

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