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6.2 Probability Theory

6.2 Probability Theory. Binomial Theory and Birthday problem. Ex 1- 3 coins. Ex 1: You plan to toss 3 coins. Let X=# heads. p=______ q=_______ n=_______ Find: P(X=1)= P(X=2)= P(X=3)= Mean= μ= np = Standard deviation = σ = ( npq ) =. table.

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6.2 Probability Theory

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  1. 6.2 Probability Theory Binomial Theory and Birthday problem

  2. Ex 1- 3 coins Ex 1: You plan to toss 3 coins. Let X=# heads. p=______ q=_______ n=_______ Find: P(X=1)= P(X=2)= P(X=3)= Mean= μ= np = Standard deviation = σ=(npq)=

  3. table

  4. Ex 2: Assume that the probability you like a course is 70%. You plan to take 5 courses. Let X=# of courses you like this semester. p=______ q=_______ n=_______ Find: P(X=0)= P(X=1)= P(X=2)= P(X=3)= P(X=4)= P(X=5)= P(X>=1)= P(X>=2)= Mean= μ= np = Standard deviation = σ=(npq)=

  5. Ex.3: Assume that each time you send out a resume, the probability you get an interview is 30%, if you send out 5 resumes, find the probability you will receive: At least one interview At least two interviews Mean= μ= np = Standard deviation = σ= =

  6. Birthday problem • Let E = probability that at least 2 of us have the same birthday • E complement = = ? • Recall: P(E) = 1 – P( ) • For n= 5: Find P( )= • Find P(E) • For n=13: Find P( )= • Find P(E) • For n=40: Find P( )= • Find P(E)

  7. Birthday problem- for larger n

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