The ABC association has 70 members 25 of the members are Californian, 30 of memb
ID: 3266033 • Letter: T
Question
The ABC association has 70 members 25 of the members are Californian, 30 of members are Vegetarian and 15 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? ExplainExplanation / Answer
Total members = 70
Let, A=from California
B=Vegetarian
We know that N(A)=25, N(B)=30, N(A and B)=15
Thus, N(A or B)=N(A)+N(B)-N(A and B)=25+30-15=40
a) P(A or B)=40/70=4/7
b) P(B and not A)=P(B)-P(B and A)=(30-15)/70=15/70
c) P(neither A nor B)=1-P(A or B)=1-4/7=3/7
d) P(not B | A)= P(not B and A)/P(A)= [P(A)-P(A and B)]/P(A)= (25-15)/25=10/25=2/5
e) P(A and B) is not equal to P(A)*P(B) therefore they are not independent
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