A compact disc is placed in a player that randomly selects and plays songs from the disc.The compact disc contains 3 ballads, 4 instrumental pieces,X dance tracks and no other pieces.If the probability that the first song played will be a ballad is 1/4,what is the value of X?
could you show me how to do it
one hitch is that there are only 3 ballads.
Anyway, peter, fix that and redo Reiny's calculations to find that x=5.
As for my hint, since there must be 12 songs in all, the missing x pieces must total 5.
4/(x+7)=1/4
x+7=16
x=9
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To find the value of X, we need to determine the total number of songs on the compact disc. We know that the probability of the first song being a ballad is 1/4.
Let's consider the total number of songs:
Number of ballads = 3
Number of instrumental pieces = 4
Number of dance tracks = X
The probability of selecting a ballad as the first song is 1/4. This means that out of the total number of songs, one-fourth should be ballads.
So, the equation to represent this probability is:
(Number of ballads) / (Total number of songs) = 1/4
Therefore, we have:
3 / (3 + 4 + X) = 1/4
To solve for X, we can cross-multiply:
3 * 4 = 1 * (3 + 4 + X)
12 = 3 + 4 + X
Combine like terms:
12 = 7 + X
Subtract 7 from both sides:
12 - 7 = X
Simplifying:
5 = X
Therefore, the value of X is 5.
is it 3 / 1/4 = 12 ?
pieces on disc
= 3 + 4 + x
= x+7
prob of picking one of the 4 ballads
= 4/(x+7)
but we are told
4/(x+7) = 1/4
x+7 = 16
x = 9