Question

the chess club has 8 members. a new captain will be chosen by randomly selecting the name of one of the members. leah and luke both want to be captain. leah says the chance that she will be chosen as captain is \\(\frac{1}{2}\\) because she is either chosen for captain or she is not. luke says the chance that he is chosen is \\(\frac{1}{8}\\).

b. construct arguments do you agree with lukes statement? use a mathematical argument to justify your answer.

Explanation:

Determine the total number of outcomes

$$ n(S) = 8 $$

Calculate the probability of selecting Luke

$$ P(\text{Luke}) = \frac{1}{8} $$

Compare the calculated probability with Luke's statement

$$ \frac{1}{8} = \frac{1}{8} $$

Answer:

Yes, I agree with Luke's statement. Since there are 8 members in the Chess Club and each member has an equal chance of being randomly selected, the probability of Luke being chosen is 1 out of 8, which is \(\frac{1}{8}\).