Please show all steps. Thank you!! The ABC association has 60 members. 25 of the

Question

Please show all steps. Thank you!! The ABC association has 60 members. 25 of the members are Californian, 30 of the members are Vegetarian and 10 of the members are both Californian and Vegetarian. If you randomly select one person from this association what is the probability that (a) The person is Californian or Vegetarian? (b) The person is Vegetarian but not Californian? (c) The person is neither Californian or Vegetarian? (d) If the person selected is Californian that she/he is not Vegetarian? (e) Are the events Californian and Vegetarian independent? Explain

Explanation / Answer

a)

P(A or B) = P(A) + P(B) - P(A and B)

= 25/60 + 30/60 - 10/60

= 0.75

b)

people who are vegetarian and not Californian

= B - (A and B)

= 30 - 10

= 20

probability = 20/60 = 0.3333

c)

people who are neither Californian or vegetarian

= 60 - 45

= 15

probability = 15/60 = 0.25

d)

P( B’ and A) = A - (A and B) = 25 - 10 = 15 /60 = 0.25

P(B’|A) = P(B’ and A) / P(A)

= 0.25/25/60

= 0.6

e)

P(A) * P(B) = 25/60 * 30/60 = 5/25 != P(A and B)

hence it is not independent

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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