Random Patriotism
You have a bag containing 15 red beads; 15 white beads and 15 blue beads. You randomly select one bead at a time and place each one end to end on a table. What is the probability that the first nine beads you withdraw will be -in order- red, white, blue, red, white, blue, red, white, blue. Express in percent.
The answer is 0.006.
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1 solution
This is a conditional probability problem. The probability of first drawing a red bead is (15/45). The probability of then drawing a white bead would be (15/44), because you've reduced the total bead count from 45 to 44. The probability of then drawing a blue bead would then be (15/43), as the bead count has diminished by two. Then, the probability of then drawing a second red bead is (14/42). The chances of the next one being white would be (14/41), and then the next one being blue would be (14/40). Then, the chance of drawing a red bead would be (13/39), the chance of then drawing a white bead would be (13/38) and then another blue bead (13/37). Multiplying all these probabilities together yields 0.00006. Multiplying by 100 yields the percent chance:
0.006