Question

The probability that a college student belongs to a health club is 0.3. The probability that a college student lives off-campus is 0.4. The probability that a college student belongs to a health club and lives off-campus is 0.12. Find the probability that a college student belongs to a health club OR lives off-campus. Tip: P(A or B) = P(A) + P(B) - P(A and B) 0.54 0.58 0.70 0.82

Answer 1

The correct option is 2.

Explanation:

Let A be the event that the college student belongs to a health club and B be the event that the college student lives off-campus.

The probability that a college student belongs to a health club is 0.3.

`P(A)=0.3`

The probability that a college student lives off-campus is 0.4.

`P(B)=0.4`

The probability that a college student belongs to a health club and lives off-campus is 0.12.

`P(A\cap B)=0.12`

The probability that a college student belongs to a health club OR lives off-campus is

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

`P(A\cup B)=0.3+0.4-0.12`

`P(A\cup B)=0.58`

The probability that a college student belongs to a health club OR lives off-campus is 0.58. Therefore the correct option is 2.