Answer:
The probability of the first two songs being songs we liked is [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
We want to figure out the probability of the first two random songs that are played being one of the three songs that we liked. Since there are a total of 7 songs and we like 3 then the probability of the first song played being one we like is [tex]\frac{3}{7}[/tex]
Since every song gets played only once at random, we are left with 6 total songs, 2 of which we like. Therefore the probability of the second song being one of the ones we like is, [tex]\frac{2}{6}[/tex]
Now, since we need to find the probability of the first two consecutive songs being songs we like then we need to multiply both probabilities together.
[tex]\frac{3}{7} * \frac{2}{6} = \frac{3*2}{7*6}[/tex]
[tex]\frac{3*2}{7*6} = \frac{6}{42}[/tex]
We see now that the probability is [tex]\frac{6}{42}[/tex] , which we can simplify even more by dividing the numerator and denominator by a number that they can both be divided by evenly like 6.
[tex]\frac{6/6}{42/6} = \frac{1}{7}[/tex]
Finally, we can see that the probability of the first two songs being songs we liked is [tex]\frac{1}{7}[/tex]
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
