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Understanding Mutually Exclusive Events in Probability Theory

Learn about mutually exclusive events in probability theory and how to calculate probabilities using the Addition Rule. Practice problems included.

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Understanding Mutually Exclusive Events in Probability Theory

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  1. Section 7.1 – Day 2

  2. Mutually Exclusive Events • Two events A and B are mutually exclusive if A and B cannot happen at the same time. • Event A: Roll a 3 on a die. • Event B: Roll a 4 on a die. • Mutually Exclusive • Event A: Roll a 3 on a die. • Event B: Roll an odd number on a die. • Not Mutually Exclusive

  3. Mutually Exclusive Events • Event A – Randomly select a blood donor with type O blood. • Event B – Randomly select a female blood donor. • Not Mutually Exclusive • Event A – Randomly select a Ford truck. • Event B – Randomly select a Chevy truck. • Mutually Exclusive

  4. The Addition Rule • The probability that events A or B will occur P (A or B) is given by P(A or B) = P(A) + P(B) – P(A and B) • If events A and B are mutually exclusive, the rule can be simplified to P(A or B) = P(A) + P(B).

  5. The Addition Rule • You select a card from a standard deck (52). Find the probability of selecting a 4 or an ace: • P (4 or ace) = P(4) + P(ace) = 4/52 + 4/52 = 8/52 ~0.152 • You roll a die. Find the probability of rolling a number less than 3 or rolling an odd number: • P (less than 3 or odd) = P(less than 3) + P(odd) – P(less than 3 and odd) • =2/6 + 3/6 – 1/6 = 4/6 ~ 0.67

  6. Group Work • White Book: Page 145-147…#9-14, 17-20.

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