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.
  • #1
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.
 

FAQ: A bag contains two red beads and two green beads

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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