What is the probability of selecting a white ball from a box?

In summary, the probability of drawing a fourth white ball from a box containing 10 bass with 4 white and 6 black balls, after 3 balls have already been removed (with unknown color), is 0.3905. However, this question may be a trick question as it is not specified whether the previous 3 balls were replaced or not. If they were replaced, the probability would be 0.2, and if they were not replaced, the probability would be 0.3905.
  • #1
duki
264
0

Homework Statement



A box has 10 bass, 6 are black and 4 are white. Three balls are removed from the box, color unknown. Find the probability that a fourth ball removed will be white.

Homework Equations



The Attempt at a Solution



I got:
[tex]\frac{4}{10} * \frac{3}{9} * \frac{2}{8} * \frac{1}{7} = 0.00476[/tex]
 
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  • #2
duki said:

The Attempt at a Solution



I got 0.00476?
How?
 
  • #3
updated
 
  • #4
Ah, I see. You used 4/10, 3/9, and 2/8 as the probability for the first three balls - but those are the probabilities of picking all white balls. What if the first ball picked is black? Or if the second ball picked is black? Or if all of the first three are black? You haven't accounted for any of those possibilities.

You should first figure out how many different possibilities there are for the colors of the first 3 balls.

Then, once you've done that, for each of those possibilities, calculate the probability that the first three balls are those colors and then the fourth ball is white.

Finally, since those are mutually exclusive possibilities (the first three balls are either WWW, WWB, WBW, ... but only one of those), you can add up the probabilities for all the cases.
 
  • #5
Ok, I got 0.3905?
 
  • #6
duki said:

Homework Statement



A box has 10 bass, 6 are black and 4 are white. Three balls are removed from the box, color unknown. Find the probability that a fourth ball removed will be white.

As phrased this is a trick question, I think; a very good one.

As phrased, it appears that you are given no information at all about the colour of the balls that are removed, right?

Think about this. Suppose you take two balls out of the box, in the dark, and put them in two paper bags. Now switch on the light, and look at your bags.

What is the probability that the ball in the first bag is white?
What is the probability that the ball in the second bag is white?

Cheers -- sylas
 
  • #7
duki said:
Ok, I got 0.3905?
That's not quite what I got. What did you add up? (Remember you have to show your work for as long as you continue to want help!)

I think sylas has in mind a different way of reasoning, trickier but shorter... I didn't mention that at first because I figured there was more educational value in doing it the straightforward way. :wink:
 
  • #8
Without showing my work, I got 0.2.
Not sure if I'm right though.
 
  • #9
zgozvrm said:
Without showing my work, I got 0.2.
Not sure if I'm right though.

I got twice as much as that...
 
  • #10
sylas said:
I got twice as much as that...

After re-calculating, so did I!
 

1. What is the probability of selecting a red ball from a box of 10 balls?

The probability of selecting a red ball from a box of 10 balls depends on the number of red balls in the box. If there are 3 red balls in the box, the probability would be 3/10 or 30%.

2. If I have a box of 20 balls and 8 of them are blue, what is the probability of selecting a blue ball?

The probability of selecting a blue ball from a box of 20 balls would be 8/20 or 40%. This assumes that the balls are randomly mixed and there is no bias towards any particular color.

3. How many different combinations of balls can be selected from a box of 5 red balls and 3 blue balls?

There are 56 different combinations of balls that can be selected from a box of 5 red balls and 3 blue balls. This can be calculated using the combination formula nCr = n! / (r!(n-r)!), where n is the total number of balls and r is the number of balls being selected.

4. What is the probability of selecting 2 red balls in a row from a box of 10 balls if one red ball has already been selected?

The probability of selecting 2 red balls in a row from a box of 10 balls would depend on the total number of red balls in the box. If there are 3 red balls in the box, the probability would be (3/10) * (2/9) or approximately 6.67%.

5. How does the number of balls in a box affect the probability of selecting a specific color?

The number of balls in a box can affect the probability of selecting a specific color in two ways. First, a larger number of balls means a larger pool to select from, which can decrease the probability of selecting a specific color. Second, if there are more balls of a specific color in the box, the probability of selecting that color would increase.

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