Question

2) You win the grand prize typically once in every 100 entries. If you enter the sweepstakes 1,000 times, how many times would you expect to win the grand prize?3) There is a 5% chance of snow in Florida this year. If there are 365 days in the year, how many days is it expected to snow?

Answer 1

The question is a Probability problem.

The Probability of an event, E, is given by:

`Pr(E)=\text{ }\frac{number\text{ of expected outcomes}}{\text{Total number of outcomes}}`

For sentence 1, in the question, we have:

`\begin{gathered} Pr(w\text{inning the grand prize)=}(1)/(100) \\ Pr(\text{winning the grand prize)=0.01} \end{gathered}`

For sentence 2, the new total number of outcomes is 1000.

Thus, we have:

`\begin{gathered} Pr(\text{winning the grand prize)=}\frac{number\text{ of expectations}}{1000} \\ 0.01=\frac{number\text{ of expectations}}{1000} \\ \text{number of expectations=0.01}*1000 \\ \text{number of expectations=10} \end{gathered}`

Hence, the number of times that is expected to win the grand prize is 10times