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

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

Answer 2

0.014%

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=(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)((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)((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%