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3 May, 02:20

Your band is one of 8 bands competing at the battle of the bands. The order of the performances is determined at random. The first 5 performances are on Friday night and the next 3 are on Saturday.

What is the probability that your band gives the last performance on Friday night and your rival band performs immediately before you?

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  1. 3 May, 05:27
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    1.79 %.

    Step-by-step explanation:

    you have to calculate the probability of a series of events before you can calculate the final probability.

    The first event is that the band plays on Friday.

    If there are 8 bands, but only 5 play on Friday, then the probability that they will play on Friday is

    5/8

    Now, the second event that they are the last ones is 1/5, since they are 5 bands.

    Therefore the probability that they will play on Saturday and last is

    5/8 * 1/5 = 1/8

    Now, for the rival band it would be, knowing that on Friday there is already a quota assigned and one band less, the probability that they will play that day is

    4/7

    as they play before the other group, it would be 1/4, as there is already a quota assigned.

    The final probability would then be:

    4/7 * 1/4 = 1/7

    Now the probability that the band gives the last performance on Friday night and your rival band performs immediately before them, is:

    1/8 * 1/7 = 0.0179

    That is 1.79 %.
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