A bag contains 5 black, 4 white and x red marbles. If the probability of picking a red marble is 2/3, find the value of x
Answer Details
Let's start by using the total number of marbles in the bag which is the sum of the number of black, white, and red marbles.
Total number of marbles = 5 (black) + 4 (white) + x (red) = 9 + x
Now, we are given that the probability of picking a red marble is 2/3. This means that out of all the marbles in the bag, 2/3 of them are red.
So, we can write an equation using this information:
Number of red marbles / Total number of marbles = 2/3
Simplifying this equation, we get:
x / (9 + x) = 2/3
Cross-multiplying, we get:
3x = 2(9 + x)
Simplifying this equation, we get:
3x = 18 + 2x
Subtracting 2x from both sides, we get:
x = 18
Therefore, the value of x is 6.
So, there are 6 red marbles in the bag.