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Question relating to probablilties

  1. Dec 1, 2003 #1
    I have a test tomorrow and there are 2 question I am stuck on

    Five patrons check their coats at a theatre. In the confusion at the end of the performance, the attendant, in despair, hands the coats back at random

    What is the probability taht 3 or more of the patrons will get their coat back.

    The hint given is: can exactly 4 people receive their correct coat? Im pretty sure they cant because to do that, the fifth person would get the right coat back as well.

    second one:

    You are doing some wordprocessing, and you accidentally type 3 letters if the alphabet without noticing which ones you typed. What is the probability that the letters will be in alphabetical order from left to right?

    So can anyone help? I knoe what the asnwers are, i just dotn know how to get them (the answer is 11/120 and 1/6)

    somone, please explain!!!!
     
    Last edited: Dec 1, 2003
  2. jcsd
  3. Dec 2, 2003 #2
    1.
    This means that there is a single case when 4 or more of the patrons will get their coat back.

    In how many ways can the attendant hand back the coats?

    N=permutations of 5=5!=120

    Next it must be calculated the number of possible cases when the attendant hands exactly 3 correct coats back.

    N[3]=C53=5!/(3!)*(5-3)!=10

    The probability that 3 or more of the patrons will get their coat back is:

    P=(N[3]+1)/120=11/120


    2.I assume that the three letters are distinct.Whatever letters are typed we can form 3!=6 distinct possibilities with them,function of their position (on the first,second or third place).

    For example if the three letters were a,d,e we have the possibilities:

    a,d,e
    a,e,d
    d,e,a
    d,a,e
    e,a,d
    e,d,a

    In how many cases are they in the alphabetical order?In exactly one case.

    Hence the seeked probability is:P=1/6.

    The same is valid no matter the letters written,assuming they are distinct.
     
    Last edited: Dec 2, 2003
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