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?

Answer 1

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%

Answer 2

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