Question

question 1 (multiple choice worth 2 points) (likelihood mc) a group of students were asked which club they planned to join. compare the probabilities of a randomly selected student joining a club and interpret the likelihood. choose the statement that is true.
club percent of students
garden club 0.1
robotics club 0.2
technology club 0.5
zoology club 0.2
the student will be more unlikely to join the garden club than the robotics club because p(garden) < p(robotics).
the student will be more likely to join the zoology club than the robotics club because p(zoology) > p(robotics).
the student will be equally likely to join the robotics club or technology club because p(robotics) = p(technology).
the student will be more unlikely to join the robotics club than the garden club because p(robotics) < p(garden).

Explanation:

Step1: Identify probabilities

The probability of joining the Zoology Club $P(\text{Zoology}) = 0.2$, the Technology Club $P(\text{Technology})=0.5$, the Robotics Club $P(\text{Robotics}) = 0.2$ and the Garden Club $P(\text{Garden})=0.1$.

Step2: Compare probabilities

We see that $P(\text{Zoology}) = P(\text{Robotics})=0.2$, $P(\text{Technology}) = 0.5$ and $P(\text{Garden})=0.1$. Since $P(\text{Garden})

Answer:

The student will be more unlikely to join the Garden Club than the Robotics Club because $P(\text{Garden})