Question

# \text { Q2 } Suppose you are a famous country music artist. Every time you release a song, it lands on the Spotify Top 200 chart ("the charts") with a

probability of , independent of all other factors.For the first four parts of this question, assume that you choose to release 12 songs in 2020. Q 2.1 What is the probability that exactly half of the songs you release end up on the charts in 2020? Select all that apply. \begin{array}{l} \frac{1}{2} \\ 1-\sum_{k=0}^{5}\left(\begin{array}{c} 12 \\ k \end{array}\right)\left(\frac{2}{3}\right)^{k}\left(\frac{1}{3}\right)^{12-k}-\sum_{k=7}^{12}\left(\begin{array}{c} 12 \\ k \end{array}\right)\left(\frac{2}{3}\right)^{k}\left(\frac{1}{3}\right)^{12-k} \\ \left(\begin{array}{c} 12 \\ 6 \end{array}\right)\left(\frac{2}{3}\right)^{6}\left(\frac{1}{3}\right)^{6} \\ \left(\begin{array}{c} 12 \\ 6 \end{array}\right)\left(\frac{1}{3}\right)^{6} \\ 1-\sum_{k=0}^{5}\left(\begin{array}{c} 12 \\ k \end{array}\right)\left(\frac{2}{3}\right)^{k}\left(\frac{1}{3}\right)^{12-k} \end{array}

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