Question

seth is analyzing the number of students in his class and high school who own skateboards. he puts the data in the table shown. given the information in the table, which event is the least likely?

	freshmen	non - freshmen	total
does not own skateboard	210	840	1,050
total	250	950	1,200

skateboard ownership at seths high school

a randomly selected student who owns a skateboard is a freshmen.
a randomly selected student who does not own a skateboard is a freshmen.

Explanation:

Step1: Calculate probability of first - event

The number of students who own a skateboard is 150, and the number of freshmen who own a skateboard is 40. The probability $P_1$ that a randomly selected student who owns a skateboard is a freshman is $P_1=\frac{40}{150}=\frac{4}{15}\approx0.267$.

Step2: Calculate probability of second - event

The number of students who do not own a skateboard is 1050, and the number of freshmen who do not own a skateboard is 210. The probability $P_2$ that a randomly selected student who does not own a skateboard is a freshman is $P_2 = \frac{210}{1050}=\frac{1}{5}=0.2$.

Step3: Compare probabilities

Since $0.2<0.267$, the event “A randomly selected student who owns a skateboard is a freshman” has a higher probability, and “A randomly selected student who does not own a skateboard is a freshman” is the least likely event.

Answer:

A randomly selected student who owns a skateboard is a freshman.