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More Probability Rules

More Probability Rules. 6.2. Addition and Multiplication Rules. P(A or B) = P(A) + P(B) if and only if A and B are disjoint P(A and B) = P(A) · P(B) if and only if A and B are independent. Roll a die one time. Find the probability of getting a four or a six.

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More Probability Rules

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  1. More Probability Rules 6.2

  2. Addition and Multiplication Rules • P(A or B) = P(A) + P(B) if and only if A and B are disjoint • P(A and B) = P(A)·P(B) if and only if A and B are independent

  3. Roll a die one time • Find the probability of getting a four or a six. • P(4 or 6) = P(4) + P(6) = 1/6 + 1/6 = 1/3 can do this  disjoint • Find the probability of getting a four or an even number • P(4 or even #) = P(4) +P(even) = 1/6+3/6 = 4/6 can’t do this  not disjoint.

  4. Multiplication Rule Example 1 • We want to know the probability of randomly choosing a BHS student and having the student be a senior girl. • Let’s assume P(girl) = ½ and P(senior) = ¼ P(girl and senior) = P(girl) ·P(senior) = ½ · ¼ = 1/8 This example works because the events are independent.

  5. Example 2 • What is the probability of randomly choosing a student from BHS and having it be a girl with long hair. • Let’s assume P(girl)=.5 and P(long hair)=.3 P(girl and long hair) = P(girl) ·P(long hair) = .5·.3 = .15 This is wrong because these events are not independent. Realistically the P(girl and long hair) would be much higher than 15%

  6. Blue eyes are recessive. That means in order to get blue eyes you must receive a blue gene from both parents. • What is the probability of a child having blue eyes if both parents have a one blue eyed gene and one brown eyed gene? ½ · ½ = ¼ Multiplication Rule • What is the probability of a child not having blue eyes? 1 – ¼ = ¾ Complement Rule

  7. If the family has two kids, what is the probability that one will have blue eyes and the other will not have blue eyes? P(blue eyes) = ¼ P(not blue) = 1 – ¼ = ¾ P(blue & not blue) ¼ · ¾ = 3/16

  8. HW #40: 6.24,26,30,34 &pg 1 of Joint Probability WS

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