A large box initially contains 5 white beads and 5 red ones. As experiment consists of the following steps: Roll a fair die twice in succession and observe the sum of the two upper face numbers. If the sum is less than or equal to 4 (Sum<4), randomly select 1 bead from the box. If the sum is greater than or equal to 10 (Sum>10), randomly select 2 beads from the box without replacement. If the sum is any other value (that is 5,6,7,8, or 9), do not select any beads. a) Calculate the probability that at least one red bead is withdrawn from the box b) Calculate the conditional probability that Sum210 given that at least one red bead is withdrawn from the box.

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