A bag contains x beads. Calculate the value of x.

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In summary, we have a bag with x beads, 6 of which are red and the rest blue. The probability of drawing 2 beads of the same color is 9/17. Using algebra, we can calculate the value of x to be 17 or 9, with 17 being the most likely solution.
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A bag contains x beads. 6 of the beads are red and the rest are blue. Ravish is going to take at random 2 beads from the bag. The probability that the 2 beads will be of the same colour is $9 /17$
Using algebra calculate the value of x. ( show sworking if possible)
 
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There are 6 red beads and x- 6 blue beads. The probability the first bead taken is red is 6/x. In that case there are 5 red beads and x- 6 blue beads left for a total of x-1 beads. The probability the second bead is also red is 5/(x- 1). The probability the two beads are both red is (6/x)(5/(x- 1))= 30/(x(x- 1)).

There are 6 red beads and x- 6 blue beads. The probability the first bead taken is blue is (x- 6)/x. In that case there are 6 red beads and x- 7 blue beads left for a total of x- 1 beads. The probability the second bead is also blue is (x- 7)/(x- 1). The probability the to beads are both blue is ((x- 6)/x)((x- 7)/(x- 1))= (x- 6)(x-7)/(x(x- 1).

The probability the two beads are the same color is 30/(x(x-1)+ ((x- 6)(x- 7)/(x(x-1))= (x^2- 13x+ 72)/(x^2- x).

Set that equal to 9/17 and solve for x.
 

FAQ: A bag contains x beads. Calculate the value of x.

1. How do you calculate the value of x in a bag of beads?

The value of x can be calculated by counting the number of beads in the bag. Each bead represents one unit, so the value of x is equal to the number of beads in the bag.

2. Can the value of x vary in different bags of beads?

Yes, the value of x can vary in different bags of beads depending on the size of the bag and the number of beads inside. It is important to count the beads in each specific bag to accurately determine the value of x.

3. How can I determine the value of x if some beads are missing?

If some beads are missing, you can estimate the value of x by calculating the average number of beads in a small sample of the bag and then multiplying that number by the total number of samples in the bag.

4. What is the significance of calculating the value of x in a bag of beads?

Calculating the value of x in a bag of beads can be important for various reasons, such as determining the cost of the beads, keeping track of inventory, or completing a math or science experiment.

5. Can the value of x change over time?

Yes, the value of x can change over time if beads are added or removed from the bag. It is important to recount the beads periodically to ensure an accurate value of x.

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