Final answer:
The probability that Casey picks 1 red bead, 1 green bead, and then 1 white bead in sequence without replacement from a box containing 4 red, 36 green, and 10 white beads is calculated by multiplying the probability of each event. The final probability is (1/50) × (9/49) × (5/24).
Step-by-step explanation:
The question asks about the probability of picking beads of different colors in a specific sequence without replacement, which involves calculating the probability of dependent events. To solve for the probability that Casey picks 1 red bead, 1 green bead, and then 1 white bead without replacing any of the beads, we need to multiply the probability of each event happening in sequence.
The probability of picking a red bead first is 4 red beads out of 50 total beads (4+36+10), or 4/50. Once the red bead is picked, there are 49 beads left, so the probability of then picking a green bead is 36 green beads out of 49 remaining beads, or 36/49. Finally, with one red and one green bead already picked and set aside, there are 48 beads remaining, with the probability of picking a white bead being 10 white beads out of 48 remaining beads, or 10/48.
To find the overall probability, we multiply these individual probabilities together:
(4/50) × (36/49) × (10/48), which simplifies to (1/50) × (9/49) × (5/24)
After computing, the final probability of Casey picking one bead of each color in the specified order without replacement is (1/50) × (9/49) × (5/24).