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Chen has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Chen's Jumble has 4 classical songs, 3 rock songs, and 2 rap songs on it. Chen is going to listen to 360 songs.
What is the best prediction for the number of times Chen will listen to a classical song?
Choose 1 answer:
(A) Exactly 90 times
(B) Close to 90 times but probably not exactly 90 times
(c) Exactly 160 times
(D) Close to 160 times but probably not exactly 160 times

Chen has an MP33 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Chen's Jumble has 44 classical songs, 33 rock songs, and 22 rap songs on it. Chen is going to listen to 360360 songs.\newlineWhat is the best prediction for the number of times Chen will listen to a classical song?\newlineChoose 11 answer:\newline(A) Exactly 9090 times\newline(B) Close to 9090 times but probably not exactly 9090 times\newline(C) Exactly 160160 times\newline(D) Close to 160160 times but probably not exactly 160160 times

Full solution

Q. Chen has an MP33 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Chen's Jumble has 44 classical songs, 33 rock songs, and 22 rap songs on it. Chen is going to listen to 360360 songs.\newlineWhat is the best prediction for the number of times Chen will listen to a classical song?\newlineChoose 11 answer:\newline(A) Exactly 9090 times\newline(B) Close to 9090 times but probably not exactly 9090 times\newline(C) Exactly 160160 times\newline(D) Close to 160160 times but probably not exactly 160160 times
  1. Calculate Total Number of Songs: Calculate the total number of songs on Chen's Jumble.\newlineTotal number of songs =Number of classical songs+Number of rock songs+Number of rap songs= \text{Number of classical songs} + \text{Number of rock songs} + \text{Number of rap songs}\newlineTotal number of songs =4+3+2= 4 + 3 + 2\newlineTotal number of songs =9= 9
  2. Calculate Probability of Selecting: Calculate the probability of selecting a classical song. Probability of selecting a classical song = Number of classical songsTotal number of songs\frac{\text{Number of classical songs}}{\text{Total number of songs}} Probability of selecting a classical song = 49\frac{4}{9}
  3. Predict Number of Times: Predict the number of times Chen will listen to a classical song.\newlineExpected number of times listening to a classical song == Probability of selecting a classical song * Total number of songs listened to\newlineExpected number of times listening to a classical song =(49)×360= (\frac{4}{9}) \times 360
  4. Perform Calculation: Perform the calculation to find the expected number of times.\newlineExpected number of times listening to a classical song = (49)×360(\frac{4}{9}) \times 360\newlineExpected number of times listening to a classical song = 4×404 \times 40\newlineExpected number of times listening to a classical song = 160160

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