Of all users of a gym facility. 72% of them use the treadmill regularly, 47% use

Question

Of all users of a gym facility. 72% of them use the treadmill regularly, 47% use the swimming pool regularly, and 34% use both the treadmill and swimming pool regularly. Suppose that you just met a person who uses the gym facility. What is the probability that the person whom you met regularly uses the treadmill, swimming pool, or both? What is the probability that the person whom you met is a regular user of the swimming pool, given that he or she uses the treadmill regularly? Are the two events "the person you met regularly uses the treadmill" and" the person you met regularly uses the swimming pool" independent? P (treadmill and swimming pool) = and P (treadmill) P (swimming pool) = These probabilities are not equal to each other. Therefore, the two events are not independent.

Explanation / Answer

a. P(treadmill or swimming pool) = P(treadmill) + P(swimming pool) - P(treadmill and swimming pool)

= 0.72 + 0.47 - 0.34 = 0.850

b. P(swimming pool | treadmill) = P(treadmill and swimming pool) / P(treadmill)

= 0.34 / 0.72 = 0.472

c. P(treadmill and swimming pool) = 0.34

P(treadmill) * P(swimming pool) = 0.72 * 0.47 = 0.338.

These probabilities are not equal to each other. The two events are not independent.

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.