A bag contains two red beads and two green beads

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In summary, the probability of all beads in the bag not being red after three replacements is 71.875%. This is calculated by taking into account the probability of pulling out two green beads in the first three replacements. A tree diagram can be used to visualize all the possible outcomes.
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Derivative86
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A bag contains two red beads and two green beads. You reach into the bag pull out a bead, replacing it with a red bead regardless of the color you pulled out. What is the probability that all beads in the bag are not red after three such replacements?
 
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  • #2
What is the probability that all beads in the bag are not red after three such replacements?

Hmmm, at a guess I'd say 71.875% :)
 
  • #3
I would think it is the probability of pulling out the two green beads in the first three replacement. So if my math is correct, it should be:

(2/4 * 1/4 * 4/4) + (2/4 * 3/4 * 1/4) + (2/4 * 2/4 * 1/4)
 
  • #4
You could draw a tree of all the possibilities.
 

1. How many total beads are in the bag?

There are four total beads in the bag.

2. What is the probability of pulling out a red bead?

The probability of pulling out a red bead is 50%, since there are two red beads and four total beads in the bag.

3. If I pull out two beads at a time, what is the probability of getting two beads of the same color?

The probability of getting two beads of the same color is 50%, since there is an equal chance of pulling out two red beads or two green beads.

4. If I pull out one bead and then another without replacing the first bead, what is the probability of getting a red bead and then a green bead?

The probability of getting a red bead and then a green bead is 50%, since the probability of getting a red bead on the first pull is 50% and the probability of getting a green bead on the second pull is also 50%.

5. What is the probability of pulling out a red bead and then a green bead if the first bead is replaced before the second pull?

The probability of pulling out a red bead and then a green bead is still 50%, since replacing the first bead does not change the probability of pulling out a red bead on the second pull.

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