1(a) You are a manager in the quality assurance department of a semiconductor ma

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? (5 marks)
1(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? (5 marks)

Explanation / Answer

Quesion 1(a) Pr(Defective electric circuits) = 0.05

Here is X is the number of defective electrical circuits out of 10.

Pr(X = 0 ; 10 ; 0.05) = 10C0 (0.05)0(0.95)10 = 0.5987

(b) Pr(win each set) = 0.6

As winning any set is independen here so if a player wins the first set he has to win only two sets out of next 4.

So,
Pr(THe player will win the match) = Pr(He wins next two sets) + Pr(he wins 1 set in next two sets and win the 4th one) + Pr(he wins one in next three and win the last set/5th set)

= BIN (2 ; 2; 0.6) + BIN (1; 2; 0.6) * 0.6 + Pr(1 ; 3; 0.6) * 0.6

= 0.62 + 2 * 0.6 * 0.4 * 0.6 + 3 * 0.6 * 0.4 * 0.4 * 0.6 = 0.8208

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