Finding the Minimum Number of White Balls in a Container with 27 Balls

In summary, we have 27 balls in the container, some of which are white and some are black. We need to determine the minimum number of white balls in the container so that the probability of drawing two white balls without replacement is less than 23/30. Using the formula for probability, we set up an inequality and solve for n, the number of white balls. The corrected exercise states that the probability of drawing two white balls without replacement is [n(n-1)]/702.
  • #1
ghostfirefox
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We have 27 balls in the container, some of which are white and some black. How many white balls in the container must be at least, so that the probability that two black balls were drawn at random without a return was less than 23/30?
 
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  • #2
ghostfirefox said:
We have 27 balls in the container, some of which are white and some black. How many white balls in the container must be at least, so that the probability that two balls were drawn at random without a draw was less than 23/30?

What?? "Two balls are drawn at random without a draw"?? What does that mean? Did you mean "two white balls are drawn without a black ball being drawn"? Is this drawing without replacement? If so let "n" be the number of white balls in the container. The probability the first ball drawn is white is n/27. If that happens there are 26 balls left in the container, n-1 of them white. The probability the second ball drawn is also white is (n-1)/26. The probability both balls are white is [n(n-1)]/702. You want to solve the inequality (n^2- n)/702< 23/30.
 
  • #3
You're right a I missed a word. I corrected the exercise. Thank for your response.
 
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FAQ: Finding the Minimum Number of White Balls in a Container with 27 Balls

How can I find the minimum number of white balls in a container with 27 balls?

The minimum number of white balls in a container with 27 balls can be found by using a mathematical formula. First, determine the total number of balls in the container (27). Then, divide this number by the number of colors in the container (2). This will give you the minimum number of white balls, which in this case would be 13.5. Since you cannot have half a ball, round up to get the final answer of 14 white balls.

What is the significance of finding the minimum number of white balls in a container with 27 balls?

The minimum number of white balls in a container with 27 balls is significant because it allows you to understand the distribution of colors in the container. This information can be useful in various applications, such as predicting the likelihood of picking a white ball from the container or determining the proportion of colors in a larger sample size.

Can the minimum number of white balls in a container with 27 balls change?

Yes, the minimum number of white balls in a container with 27 balls can change depending on the total number of balls and the number of colors in the container. For example, if the container had 30 balls instead of 27, the minimum number of white balls would be 15 instead of 14.

How does the number of colors in the container affect the minimum number of white balls?

The number of colors in the container directly affects the minimum number of white balls. The more colors there are in the container, the smaller the minimum number of white balls will be. This is because the total number of balls is divided among more colors, resulting in a smaller proportion of white balls.

Is there a scientific method for finding the minimum number of white balls in a container with 27 balls?

Yes, there is a scientific method for finding the minimum number of white balls in a container with 27 balls. This method involves using a mathematical formula to determine the minimum number of white balls based on the total number of balls and the number of colors in the container. It is a reliable and accurate method for finding the minimum number of white balls.

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