Question

UP - Utle ISL LOSS? U what is the probability you will be out after the first toss? (C) What is the probability that no one will be out after the first toss? . A particular electronic device is known to contain only 10-, 22-, and 48-22 resistors, but these resistors may have 0.25-, 0.5-, or 1-W ratings, depending on how purchases are made to minimize cost. Historically, it is found that the probabilities of the 10-12 resistors being 0.25, 0.5, or 1 W are 0.08, 0.10, and 0.01, respectively. For the 22-2 resistors the similar probabilities are 0.20, 0.26, and 0.05. It is also historically found that the probabilities are 0.40, 0.51, and 0.09 that any resistors are 0.25, 0.50, and 1 W, respectively. What are the probabilities that the 48-52 resistors are (a) 0.25, (b) 0.50, and (c) 1W? 17

Answer 1

Given,

P(0.25 W) = 0.40

-> P(10 ohm resistor being 0.25 W) + P(22 ohm resistor being 0.25 W) + P(48 ohm resistor being 0.25 W) = 0.40

-> P(48 ohm resistor being 0.25 W) = 0.40 - 0.08 - 0.20 = 0.12

P(0.50 W) = 0.51

-> P(10 ohm resistor being 0.50 W) + P(22 ohm resistor being 0.50 W) + P(48 ohm resistor being 0.50 W) = 0.51

-> P(48 ohm resistor being 0.50 W) = 0.51 - 0.10 - 0.26 = 0.15

P(10 W) = 0.09

-> P(10 ohm resistor being 1 W) + P(22 ohm resistor being 1 W) + P(48 ohm resistor being 1 W) = 0.09

-> P(48 ohm resistor being 1 W) = 0.09 - 0.01 - 0.05 = 0.03

Thus, (a) 0.12

(b) 0.15

(c) 0.03