Question

Luca decides to play Wheel of Letter. To play the game, contestants spin a wheel with 26 equal sections, lettered A through Z. If the pointer lands on any letter in the phrase "COUNTY FAIR," the contestant wins a prize.

Answer 1

Step-by-step explanation:

Part A

In the English alphabets, there are 26 alphabets lettered A to Z

If the pointer lands on the phrase COUNTY FAIR. There are 10 alphabets in this case

Then we compute the probability as follow

`\text{probability}=\frac{\text{number of possible outcomes}}{Total\text{ number of outcomes}}`

`\text{probability}=\frac{\text{number of possible outcomes}}{Total\text{ number of outcomes}}=(10)/(26)=(5)/(13)`
`\text{The probability is }(5)/(13)\text{ (Theoretical probability)}`

Part B

We are told that 12 of the 52 contestants exactly won the game.

Then to calculate the expected number of winners will be

`\begin{gathered} \text{Expected value=Probability}* n\\u mber\text{ of contestant} \\ \text{Expected value =}(5)/(13)*52=20 \end{gathered}`

Therefore, the expected number of winners will be 20 winners

The actual number of winners are 12

Theoretically, 20 contestants won but in an actual sense, there are only 12 winners

Therefore, there have to be 8 more winners for the experimental probability to approach theoretical probability