A bag contains 11 red balls, 9 blue balls and x yellow balls. The probabilty of choosing a yellow ball at random is 1/6. What is the probability of not getting a blue ball.

i think there 4 yellows

prob(yellow) = x/(20+x)

but we know this is 1/6

x/(20+x) = 1/6
6x = 20+x
x = 4

so there are 24 balls, of which 9 are blue

so Prob(blue) = 9/24 = 3/8

To find the probability of not getting a blue ball, we need to determine the number of balls that are not blue and then divide it by the total number of balls in the bag.

The total number of balls in the bag is given by the sum of red balls, blue balls, and yellow balls:
Total number of balls = number of red balls + number of blue balls + number of yellow balls

From the given information, we know that there are 11 red balls and 9 blue balls. We also know that the probability of choosing a yellow ball is 1/6. Let's represent the number of yellow balls as x.

So, the total number of balls can be written as:
Total number of balls = 11 + 9 + x

Now, we need to find the probability of not getting a blue ball. This means selecting either a red ball or a yellow ball.

The probability of not getting a blue ball is equal to 1 minus the probability of selecting a blue ball:
Probability of not getting a blue ball = 1 - Probability of selecting a blue ball

The probability of selecting a blue ball can be found by dividing the number of blue balls by the total number of balls:
Probability of selecting a blue ball = (number of blue balls) / (total number of balls)

Substituting the known values, we have:
Probability of selecting a blue ball = 9 / (11 + 9 + x)

Finally, the probability of not getting a blue ball becomes:
Probability of not getting a blue ball = 1 - (9 / (11 + 9 + x))

You can simplify this expression further if you know the value of x.