Question

A bag contains two red beads and two green beads. You reach into the bag and 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 red after three such replacements

Answers

  1. The probability that all beads in the bag are red after three replacement is 1/8.
    According to the given question.
    Total number of red beads = 2
    Total number of green beads = 2
    Total number of beads in a bag = 4
    Now, the probability of pulling out red bead = 2/4 = 1/2
    the probability of pulling out second bead as red with repalcement
    = 2/4
    = 1/4
    Similarly, the probability of pulling out the third bead with replacement which is also red
    = 2/4
    = 1/2
    Therefore, the probability that all beads in the bag are red after three replacement
    = 1/2 × 1/2 ×1/2
    = 1/8
    Hence, the probability that all beads in the bag are red after three replacement is 1/8.
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