Square numbers probability help

[david18]

Hi, I am trying to solve a question on a past paper; here is one that is very similar to it- http://www.gcsemathspastpapers.com/images/p5j04q19.htm

Im presuming the probability of blue marbles is 7/(k+7)

On part (d) would i have to do something like:

7/(k+7) x k/(k+7) = 4/9 ?

Ive tried the above equation but it doesn't seem to work out seeing as it doesn't give me any square numbers as the LCM becomes 9(k+7)

any help would be much appreciated.

 

[drpizza]

You're correct for the probability of blue.

For the second part, you're really close. You have the probability that the first girl gets blue and the 2nd girl gets red. Isn't there something else that could happen such that they still have different colors? (Then, simplify and cross multiply)

edit:
You have $$\frac{7}{k+7}*\frac{k}{k+7} = \frac{4}{9}$$

= $$\frac{7k}{(k+7)^2}=\frac{4}{9}$$

Are you sure you don't end up with a $$k^2$$ term in there?

 

[Architeuthis Dux]

Hello, based on the information provided, it seems like you are trying to solve a probability problem involving blue marbles and square numbers. It is not clear what the specific question is, but I can provide some general guidance on approaching this type of problem.

First, it is important to understand the concept of probability. Probability is a measure of the likelihood of an event occurring. In this case, the event is selecting a blue marble from a bag of marbles. The probability is calculated by dividing the number of desired outcomes (blue marbles) by the total number of outcomes (total number of marbles).

In the given link, the question states that there are 7 blue marbles out of a total of k+7 marbles. Therefore, the probability of selecting a blue marble is 7/(k+7).

In part (d) of the question, it seems like you are trying to calculate the probability of selecting two blue marbles in a row. In this case, you would need to multiply the probability of selecting a blue marble on the first try (7/(k+7)) by the probability of selecting a blue marble on the second try, which would be (7-1)/(k+7-1) or 6/(k+6). This is because after the first marble is selected, there would be one less blue marble and one less total marble in the bag.

Therefore, the overall probability of selecting two blue marbles in a row would be (7/(k+7)) x (6/(k+6)) = 42/(k+7)(k+6). This is the general approach for calculating the probability of multiple events occurring in a row.

As for the issue with the LCM becoming 9(k+7), it is important to note that the LCM is not necessary for solving this problem. The LCM is only used when finding a common denominator for fractions, but in this case, we are not adding or subtracting fractions.

I hope this helps to clarify the approach for solving this type of problem. If you have any further questions or need additional assistance, please don't hesitate to reach out. Best of luck!