Given the digits 2, 3, 4, 5, 6 and 8, how many four-digit number can be formed (

Question

Given the digits 2, 3, 4, 5, 6 and 8, how many four-digit number can be formed (a) if the number must be even and no repetition? (b) if the digits 5 and 6 must appear in the number and in that order and with no repetition? In a certain factory, machine A, B and C produce 2%, 1% and 3% defective spring respectively. If the total production of springs in this factory, machine A produces 35%, machine B produces 25%, an produces 40%. If one spring is selected at random, find (a) the probability that it is defective? (b) if the selected spring is defective, find the probability that it was produced by machine C

Explanation / Answer

8)a) No of ways to form four digit number = 3 * 4 * 5 * 4 = 240

b) No of ways = 1 * 1 * 4 * 3 + 4 * 1 * 1 * 3 + 4 * 3 * 1 * 1 = 36

9) a) P(it is defective) =P(defective | A) * P(A) + P(defective | B) * B + P (defective | C) * C

= 0.02 * 0.35 + 0.01 * 0.25 + 0.03 * 0.4

= 0.0215

B ) P(machine C | defective) = P(defective | C) * C / defective

= 0.03 * 0.4 / 0.0215 = 0.56

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