Statistics- Unfair Coin Toss

• Nov 11th 2012, 09:59 AM
CollegeBug
Statistics- Unfair Coin Toss
An "unfair" coin has a heads side which weighs two and one-half times heavier than the tails side. If you toss this unfair coin 100 times, how many of those times would you expect to see heads? Explain why.
• Nov 11th 2012, 10:25 AM
richard1234
Re: Statistics- Unfair Coin Toss
Assuming the weight condition implies, "the probability of obtaining a head is 2 1/2 times that of obtaining a tail," what is the probability of obtaining a head?
• Nov 11th 2012, 03:46 PM
Soroban
Re: Statistics- Unfair Coin Toss
Hello, CollegeBug!

Quote:

An "unfair" coin has a Heads side which weighs two-and-a-half times heavier than the Tails side.
If you toss this unfair coin 100 times, how many of those times would you expect to see Heads?

The Heads side is $\displaystyle 2\tfrac{1}{2}$ times heavier than the Tails side.

The Heads side will be on the bottom $\displaystyle \tfrac{5}{7}$ of the time.

Hence: .$\displaystyle \begin{Bmatrix}P(\text{Tails}) &=& \frac{5}{7} \\ \\[-4mm] P(\text{Heads}) &=& \frac{2}{7} \end{Bmatrix}$

We expect to see Heads: .$\displaystyle \tfrac{2}{7} \times 100 \:=\:28\tfrac{4}{7}$ times.