Noam chose 3 songs from a pile of 20 songs to play at a piano recital. What is the probability that she chose The Entertainer, Something Doi

Question

Noam chose 3 songs from a pile of 20 songs to play at a piano recital. What is the probability that she chose The Entertainer, Something Doing, and The Ragtime Dance?

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Elliana 1 week 2021-09-15T20:59:46+00:00 2 Answers 0

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    0
    2021-09-15T21:01:35+00:00

    |\Omega|={_{20}C_3}=\dfrac{20!}{3!17!}=\dfrac{18\cdot19\cdot20}{2\cdot3}=1140\\|A|=1\\\\P(A)=\dfrac{1}{1140}\approx0.09\%

    0
    2021-09-15T21:01:44+00:00

    Answer:

    0.014%

    Step-by-step explanation:

    To calculate the probability that she chooses that exact songs for the piano recital, you just first calculate the probability of her choosing one of them:

    Probability of 1=\frac{1}{20}=.05

    This is 5%, now you multipy this with the probability of the second song after this one, since there is one less song, the total number of outcomes should be reduced to 19:

    Probability of 2nd=(.05)(\frac{1}{19}

    Probability of 2nd=(0.05)(0.052}

    Probability of 2nd=0.002

    This would be .26%

    To calculate the probability of the third song being chosen after the first two, we have 2 less outcomes possibles, so the total number of possibilities now is reduced to 18.

    Probability of 3rd=(.0026)(\frac{1}{18}

    Probability of 3rd=(.0026)(0.055)

    Probability of 3rd=0.00014

    The probability of Noam choosing the three songs would be: 0.014%

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