Probability of picking one of several balls of one of two colors

So the probability is still 2/3 because there are still 4 yellow balls and 2 green balls in the bag, regardless of what was discarded. In summary, the probability of getting a yellow ball from an urn containing four yellow balls and two green balls is 2/3, both when randomly choosing a ball and when randomly choosing and discarding two balls and then choosing a third without looking at the discarded balls.
  • #1
sara_87
763
0
An bag contains four yellow balls and two green balls. Find the probability of getting a yellow
ball if you. . .
(a) . . . randomly choose a ball from the urn.
(b) . . . randomly choose and discard two balls and then choose a third.

i know how to do part a..it's just 4/6 = 2/3
but for part b, i can't do it because there will be three cases: discarding 2 yellow, discarding 2 green or discarding 1 yellow and 1 green but i should only get 1 answer
?
 
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  • #2
For part (b) you will find it easier to do if you assume that you DON'T look at the 2 balls you discarded. In this way you will see the answer is still 2/3.
 
  • #3
but how did you get 2/3 ?
i tried to work it but couldn't know how??
 
  • #4
If you don't know what the 2 discarded balls are, then the reasoning for (b) is identical to the reasoning for (a).
 

FAQ: Probability of picking one of several balls of one of two colors

What is the probability of picking one red ball out of a bag of 10 balls, where 5 are red and 5 are blue?

The probability of picking one red ball out of a bag of 10 balls, where 5 are red and 5 are blue, is 1/2 or 50%. This is because there are equal chances of picking a red or blue ball.

If I pick 2 balls out of a bag of 10 balls, where 5 are red and 5 are blue, what is the probability that both balls will be blue?

The probability of picking 2 blue balls out of a bag of 10 balls, where 5 are red and 5 are blue, is 1/4 or 25%. This is because the probability of picking one blue ball is 1/2, and the probability of picking a second blue ball is also 1/2. Therefore, the probability of both events happening is 1/2 x 1/2 = 1/4.

If I have a bag of 10 balls, where 5 are red and 5 are blue, and I pick one ball at a time without replacement, what is the probability that I will pick a red ball on the first pick and a blue ball on the second pick?

The probability of picking a red ball on the first pick and a blue ball on the second pick, without replacement, is 1/2 x 1/2 = 1/4 or 25%. This is because on the first pick, there is a 1/2 chance of picking a red ball, and on the second pick, there is a 1/2 chance of picking a blue ball.

If I have a bag of 10 balls, where 5 are red and 5 are blue, and I pick one ball at a time with replacement, what is the probability that I will pick a red ball on the first pick and a blue ball on the second pick?

The probability of picking a red ball on the first pick and a blue ball on the second pick, with replacement, is 1/2 x 1/2 = 1/4 or 25%. This is because on each pick, there is a 1/2 chance of picking a red or blue ball.

What is the probability of picking at least one red ball out of a bag of 10 balls, where 5 are red and 5 are blue?

The probability of picking at least one red ball out of a bag of 10 balls, where 5 are red and 5 are blue, is 1/2 or 50%. This is because there are equal chances of picking a red or blue ball, so the probability of picking a red ball is the same as the probability of not picking a red ball, which is 1/2 + 1/2 = 1.

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