An MP3 player is set to play songs at random from the fifteen songs it contains in memory. Any song can be played at any time, even if it is repeated. There are 5 songs by Band A, 3 songs by Band B, 2 by Band C, and 5 by Band D. If the player has just played two songs in a row by Band D, what is the probability that the next song will also be by Band D?1 in 51 in 31 in 91 in 27Not enough data to determine.
Answer: 1 in 3Explanation : The probability of playing a song by a particular band is proportional to the number of songs by that band divided by the total number of songs, or 5/15=1/3 for B and D. The probability of playing any particular song is not affected by what has been played previously, since the choice is random and songs may be repeated.
To solve this problem, we need to determine the total number of songs remaining in the MP3 player’s memory and the number of songs remaining by Band D.
There are 15 songs in total, and if two have just been played by Band D in a row, then we know that there are 13 songs remaining, of which 3 are by Band D (since there were originally 5 and 2 have already been played).
Therefore, the probability that the next song played will be by Band D is 3/13 or approximately 0.23.
So the answer is: 1 in 4, which can be written as 3 in 13, which is equivalent to the probability that the next song played will be by Band D.
Therefore, the correct answer is (C) 1 in 3.
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