Question

Please help this is for my college math 131 class

Answer 1

The probability that a randomly chosen member of the Student Government Board is a junior or lives in off-campus housing is
`\( (6)/(13) \).`

To find the probability that a randomly chosen member of the Student Government Board is a junior or lives in off-campus housing, we need to add the probabilities of these two events.

1. **Probability of being a junior (J):**

`\( P(J) = \frac{\text{Number of juniors}}{\text{Total number of students}} = (1)/(3+2+4+1+3) = (1)/(13) \)`

2. **Probability of living in off-campus housing (OC):**

`\( P(OC) = \frac{\text{Number of students in off-campus housing}}{\text{Total number of students}} = (4+1)/(3+2+4+1+3) = (5)/(13) \)`

3. **Probability of being a junior OR living in off-campus housing:**

`\( P(J \text{ or } OC) = P(J) + P(OC) = (1)/(13) + (5)/(13) = (6)/(13) \)`

So, the probability that a randomly chosen member of the Student Government Board is a junior or lives in off-campus housing is
`\( (6)/(13) \).`