Question

Suppose you just purchased a digital music player and have put 7 tracks on it. After listening to them you decide that you like 3 of the songs. With the random feature on your​ player, each of the 7 songs is played once in random order. Find the probability that among the first two songs played

Answer 1

Answer:

The probability of the first two songs being songs we liked is $\frac{1}{7}$

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 $\frac{3}{7}$

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, $\frac{2}{6}$

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.

$\frac{3}{7} * \frac{2}{6} = \frac{3*2}{7*6}$

$\frac{3*2}{7*6} = \frac{6}{42}$

We see now that the probability is $\frac{6}{42}$ , 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.

$\frac{6/6}{42/6} = \frac{1}{7}$

Finally, we can see that the probability of the first two songs being songs we liked is $\frac{1}{7}$

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