Question

seth is analyzing the number of students in his school (a high school) who own skateboards. he puts the data in the table shown. given the information in the table, which would be the most likely?
skateboard ownership at seth’s high school

	freshmen	not freshmen	total
own (and own skateboards)	210	840	1,050
total	250	950	1,200

options:
a randomly selected student who does not own a skateboard is a freshman.
a randomly selected student who does not own a skateboard is not a freshman.
a randomly selected student who owns a skateboard is a freshman.
a randomly selected student who is a freshman owns a skateboard.

Explanation:

Step1: Analyze "Does not own skateboard" and Freshmen

Total students who don't own skateboards: 150. Freshmen who don't own: 40. Probability: $\frac{40}{150}\approx0.267$. Non - freshmen who don't own: $150 - 40 = 110$. Probability: $\frac{110}{150}\approx0.733$. So "not a freshman" is more likely.

Step2: Analyze "Owns skateboard" and Freshmen

Total students who own skateboards: 1050. Freshmen who own: 210. Probability: $\frac{210}{1050}=0.2$. Non - freshmen who own: $1050 - 210 = 840$. Probability: $\frac{840}{1050}=0.8$.

Step3: Analyze "Freshman" and "Owns skateboard"

Total freshmen: 250. Freshmen who own: 210. Probability: $\frac{210}{250}=0.84$. Freshmen who don't own: 40. Probability: $\frac{40}{250}=0.16$. But we compare with other statements. The statement "A randomly selected student who does not own a skateboard is not a freshman" has probability ~0.733, which is higher than the others (0.267, 0.2, 0.84? Wait, no, wait. Wait, for "A randomly selected student who is a freshman owns a skateboard", probability is 210/250 = 0.84. Wait, let's recalculate:

Wait, the four statements:

1. "A randomly selected student who does not own a skateboard is a freshman": P(Freshman | No skateboard) = 40/150 ≈ 0.267

1. "A randomly selected student who does not own a skateboard is not a freshman": P(Not Freshman | No skateboard) = 110/150 ≈ 0.733

1. "A randomly selected student who owns a skateboard is a freshman": P(Freshman | Own skateboard) = 210/1050 = 0.2

1. "A randomly selected student who is a freshman owns a skateboard": P(Own skateboard | Freshman) = 210/250 = 0.84

Now, 0.84 is higher than 0.733? Wait, no, 0.84 is 84%, 0.733 is ~73.3%. Wait, did I miscalculate?

Wait, total freshmen: 250 (40 + 210). Total students: 1200.

Wait, "A randomly selected student who is a freshman owns a skateboard": number of freshmen who own is 210, total freshmen is 250. So 210/250 = 0.84.

"A randomly selected student who does not own a skateboard is not a freshman": 110/150 ≈ 0.733.

Wait, 0.84 is higher than 0.733. Wait, maybe I made a mistake in step 2.

Wait, let's re - express the table:

	Freshmen	Not Freshmen	Total
Own skateboard	210	840	1050
Total	250	950	1200

Now, let's calculate each probability:

1. P(Freshman | Don't own) = 40/150 ≈ 0.267

1. P(Not Freshman | Don't own) = 110/150 ≈ 0.733

1. P(Freshman | Own) = 210/1050 = 0.2

1. P(Own | Freshman) = 210/250 = 0.84

Now, 0.84 is the highest among these probabilities. Wait, so "A randomly selected student who is a freshman owns a skateboard" has probability 0.84, which is higher than 0.733. Wait, maybe I messed up the initial analysis.

Wait, the question is "which would be the most likely". So we need to find the event with the highest probability.

So let's recalculate:

• For "A randomly selected student who does not own a skateboard is a freshman": 40/150 ≈ 0.267

• For "A randomly selected student who does not own a skateboard is not a freshman": 110/150 ≈ 0.733

• For "A randomly selected student who owns a skateboard is a freshman": 210/1050 = 0.2

• For "A randomly selected student who is a freshman owns a skateboard": 210/250 = 0.84

Since 0.84 is the highest probability, this event is the most likely.

Answer:

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