Question

jeremy took at science class and received 718 points during the semester. if there were a possible 908 points in the class, what was his grade in terms of a percent?
if the probability of something is 5/7, what is it’s complement?
the probability of getting a red card from a certain box is 5 out of 14. if you picked a card and returned it each time, about how many times would you pick a red card if you did 100 picks?

Explanation:

First Sub - Question (Jeremy's grade percentage)

Step1: Recall percentage formula

To find the percentage, we use the formula $\text{Percentage}=\frac{\text{Points Earned}}{\text{Total Possible Points}}\times100\%$. Here, the points earned are 718 and the total possible points are 908.

Step2: Calculate the percentage

Substitute the values into the formula: $\frac{718}{908}\times100\% \approx 0.7907\times100\% = 79.07\%$.

Step1: Recall complement rule

The complement of an event $A$ is the event that $A$ does not occur. The formula for the complement of a probability $P(A)$ is $P(\text{complement of }A)=1 - P(A)$.

Step2: Calculate the complement

Given $P(A)=\frac{5}{7}$, then the complement is $1-\frac{5}{7}=\frac{7 - 5}{7}=\frac{2}{7}\approx0.2857$ (or as a fraction $\frac{2}{7}$).

Step1: Recall expected value formula for probability

The expected number of times an event occurs in $n$ trials is given by $E = n\times P$, where $n$ is the number of trials and $P$ is the probability of the event. Here, $n = 100$ and $P=\frac{5}{14}$.

Step2: Calculate the expected number

Substitute the values: $E=100\times\frac{5}{14}=\frac{500}{14}\approx35.71$.

Answer:

Approximately $79.07\%$ (or can be rounded to a reasonable decimal place, e.g., $79.1\%$ or $79\%$ depending on requirements)

Second Sub - Question (Complement of a probability)