coin flip

• Jun 14th 2009, 04:06 PM
brentwoodbc
coin flip
A biased (weighted) coin is designed so that the probability of a head on each flip is 3/5

If this biased coin is flipped until exactly 2 heads appear, what is the probability that it takes exactly 3 flips until the second head appears?

I drew a tree diagram but i dont really understand what it is asking for,

P(2H in 3 flips) = 36/125 But this doesnt make sense to me.
• Jun 14th 2009, 04:47 PM
pankaj
It is clear that the second head must occur on the third trial.

For the first two trials any of the following two cases are possible.
(i)H,T
(ii)T,H

Let A denote the event that exactly one head occurs in first two trials
$\displaystyle P(A)=P(H,T)+P(T,H)=\frac{3}{5}.\frac{2}{5}+\frac{2 }{5}.\frac{3}{5}=\frac{12}{25}$

Let B denote the event that head occurs on the the third trial.

$\displaystyle P(B)=\frac{3}{5}$

$\displaystyle P(A\cap B)=P(A)P(B)=\frac{12}{25}.\frac{3}{5}=\frac{36}{12 5}$

I hope it makes sense now.
• Jun 14th 2009, 05:16 PM
Plato
Quote:

Originally Posted by brentwoodbc
A biased (weighted) coin is designed so that the probability of a head on each flip is 3/5

This is purely a side bar.
It has been shown by two at Cal Tech that there is no biased coin.
Now that takes some qualifications.
By filliping or tossing a coin, we mean that the coin is rotating is the air and it is caught on the fly (while still in the air).
A simple thought experiment proves this. Image a coin spinning is air. Stop it.
There is an equal chance that it ends ups on either side regardless of weight.

I first heard of this in a lecture by a prominent author of a widely used textbook on probability and statistics. Her comment was: “the ink was dry on my new edition containing many ‘bias coin problems’ when this result hit the press”.
• Jun 14th 2009, 05:17 PM
brentwoodbc
thats good thank you.
• Jun 14th 2009, 05:40 PM
pankaj
Quote:

Originally Posted by Plato
This is purely a side bar.
It has been shown by two at Cal Tech that there is no biased coin.
Now that takes some qualifications.
By filliping or tossing a coin, we mean that the coin is rotating is the air and it is caught on the fly (while still in the air).
A simple thought experiment proves this. Image a coin spinning is air. Stop it.
There is an equal chance that it ends ups on either side regardless of weight.

I first heard of this in a lecture by a prominent author of a widely used textbook on probability and statistics. Her comment was: “the ink was dry on my new edition containing many ‘bias coin problems’ when this result hit the press”.

Can we have a biased dice
• Jun 14th 2009, 05:44 PM
brentwoodbc
Quote:

Originally Posted by Plato
This is purely a side bar.
It has been shown by two at Cal Tech that there is no biased coin.
Now that takes some qualifications.
By filliping or tossing a coin, we mean that the coin is rotating is the air and it is caught on the fly (while still in the air).
A simple thought experiment proves this. Image a coin spinning is air. Stop it.
There is an equal chance that it ends ups on either side regardless of weight.

I first heard of this in a lecture by a prominent author of a widely used textbook on probability and statistics. Her comment was: “the ink was dry on my new edition containing many ‘bias coin problems’ when this result hit the press”.

ya I guess its like if you have a 10 pound ball with a volume of .5metres and a 1 pound ball with an equal volume they fall at an equal speed, but they heavy end of things does tend to fall first