Question

freshman non - freshmen total own skateboard 40 110 150 does not own skateboard 210 840 1,050 total 250 950 1,200 a randomly selected student who is a freshmen owns a skateboard. a randomly selected student who does not own a skateboard is a freshmen. a randomly selected student who does not own a skateboard is not a freshmen. a randomly selected student who owns a skateboard is a freshmen.

Explanation:

Step1: Define conditional probability

For event A given event B: $P(A|B)=\frac{P(A\cap B)}{P(B)}$

Step2: Calculate first statement probability

Freshman who owns skateboard:
$P(\text{Own}|\text{Freshman})=\frac{40}{250}=0.16$

Step3: Calculate second statement probability

Non-owner who is freshman:
$P(\text{Freshman}|\text{No Own})=\frac{210}{1050}=0.2$

Step4: Calculate third statement probability

Non-owner who is non-freshman:
$P(\text{Non-Freshman}|\text{No Own})=\frac{840}{1050}=0.8$

Step5: Calculate fourth statement probability

Owner who is freshman:
$P(\text{Freshman}|\text{Own})=\frac{40}{150}\approx0.267$

Answer:

1. A randomly selected student who is a freshman owns a skateboard: Probability = $0.16$
2. A randomly selected student who does not own a skateboard is a freshman: Probability = $0.2$
3. A randomly selected student who does not own a skateboard is not a freshman: Probability = $0.8$
4. A randomly selected student who owns a skateboard is a freshman: Probability $\approx0.267$