MAT 133 (MATH) 4-3 Homework Questions with Solutions 2023

MAT 133 (MATH) 4-3 Homework Questions with Solutions 2023. The probability that a student has a Visa card (event V) is .60. The probability that a student has a MasterCard (event M) is .20. The probability that a student has both cards is .12. (a) Find the probability that a student has either a Visa card or a MasterCard. Formula for "OR" Probability : P(A U B) = P(A) + P(B) – P(A ∩ B) P(Visa or Mastercard) = P(Visa) + P(Mastercard) – P(Visa and Mastercard): .60 + .20 - .12 = .68 (b) In this problem, are V and M independent? We can use the Special Law of Multiplication. If P(A)•P(B) = P(A ∩ B) the events are independent If P(A)•P(B) ≠ P(A ∩ B) the events are not independent If P(Visa)•P(Mastercard) = P(Visa and Mastercard) then the events are independent. Since (.60)(.20) = .12 and they give us that P(A ∩ B)=.12, we have that V and M are independent. If these values did not match, then the events would not be independent