There are a collection of CDs. There are 2 Rock CDs, x Pop CDs and 2x + 5 Jazz CDs. A CD is chosen at random, the probability that it is Rock is 1/20. Work out the probability it is Jazz.

To answer this question first we need to work out how many CDs we have in total. We do this by adding up the number of CDs in each category:Total = 2 + x + 2x + 5.
We can simplify this to give:Total = 3x + 7The probability of a type of CD being picked is equal to the number of CDs in that category divided by the total number of CDs. So lets work with the information we have already:The probability that the CD is Rock is equal to the number of Rock CDs divided by the total number of CDs. This is 2/(3x+7).
But we know from the question that the probability is actually 1/20. So we can set them equal to each other and solve for x:1/20 = 2/(3x+7) Divide both sides by 21/40 = 1/(3x+7) Cross multiple both sides3x+7 = 40 Subtract 7 from both sides3x = 33 Divide both sides by 3x = 11The probability of the CD being Jazz is equal to (2x+5)/(3x+7). Now we just sub in our value for x and we will have the answer:(22+5)/(33+7)=27/40