Question 1 (a) You are a manager in the quality assurance department of a semico

Question

Question 1

(a) You are a manager in the quality assurance department of a semiconductor manufacturing company. Judging from recent experience, 5% of the electrical circuits produced by an automatic, high-speed machine in your company are defective. If ten electrical circuits are randomly selected, what is the probability that none of the electrical circuits are defective?  

(b) A tennis match requires that a player win three of five sets to win the match. If a player wins the first set, what is the probability that the player wins the match, assuming that the player has a 60% chance to win each set?

Explanation / Answer

a) P(a circuit is defective) = 0.05

P(a circuit is not defective) = 1 - 0.05 = 0.95

P(none of the 10 are defective) = 0.9510 = 0.5987

b) If the player wins the first game, then the player needs to win at least 2 of the next 4 sets to win the match

= 1 - P(losing more than 2 sets)

= 1 - P(losing 3 sets) - P(losing 4 sets)

= 1 - 4x0.43x0.6 - 0.44

= 1 - 0.1536 - 0.0256

= 0.8208

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