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Math Help - Discrete Probability Distribution II

  1. #1
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    Discrete Probability Distribution II

    from walpole 5.61

    Suppose the probability is 0.8 that any given person wll believe a tale about the transgressions of a famous actress.

    a) the sixth person to hear this tale is the forth one to believe it ?
    b) what is the probability that the thrd person to hear this tale is the first one to believe it ?

    i know p= 0.80 and q = 1- 0.8=0.20

    but how should i apply the above to the questions ?
    i don't even know how many people are listening to the tale.
    pls explain.
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  2. #2
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    Quote Originally Posted by hazel View Post
    from walpole 5.61

    Suppose the probability is 0.8 that any given person wll believe a tale about the transgressions of a famous actress.

    a) the sixth person to hear this tale is the forth one to believe it ?
    b) what is the probability that the thrd person to hear this tale is the first one to believe it ?

    i know p= 0.80 and q = 1- 0.8=0.20

    but how should i apply the above to the questions ?
    i don't even know how many people are listening to the tale.
    pls explain.
    a) is a negative binomial distribution problem.
    b) (0.2)(0.2)(0.8) = ....
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  3. #3
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    Hello, Hazel!

    Suppose the probability is 0.8 that any given person will believe a rumor of a scandal.

    a) What is the probability that the 6th person to hear the rumor is the 4th one to believe it ?
    Let B = the person believes the rumor.
    and N = the person does not believe the rumor.


    Among the first 5 who heard the rumor, there were 3 B's (and 2 N's).
    . . This probability is: . {5\choose3}(0.8)^3(0.2)^2

    Then the 6th person is a B: . 0.8

    Therefore: . P(\text{6th is 4th B}) \:=\:{5\choose3}(0.8)^3(0,2)^2\cdot(0.8) \;=\;0.16384




    b) What is the probability that the 3rd person to hear this rumor is the first to believe it ?

    The first two were N's: . (0.2)^2

    The third is a B: . 0.8

    Therefore: . P(\text{3rd is 1st B}) \:=\:(0.2)^2(0.8) \;=\;0.032

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, Hazel!

    Let B = the person believes the rumor.
    and N = the person does not believe the rumor.


    Among the first 5 who heard the rumor, there were 3 B's (and 2 N's).
    . .


    refering to the bold comments above, how do you know 3B and 2 N ?
    it can also be other combination ?
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