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.
Hello, CollegeBug!
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.