In a lot of 12 Microwave ovens, there are 3 defective units. A person has ordered 4 of these units and since each is identically packed

Question

B. In a lot of 12 Microwave ovens, there are 3 defective units. A person has ordered 4 of these units and since each is identically packed, the selection will be random. What is the probability that

1. all 4 units are good.
2. exactly 3 units are good
3. at least 2 units are good.

Answer 1

Given that there are 12 microwave ovens i.e., n = 12

in that 3 are defective

then number of good units = 9

The probability of good unit is = \(\frac 9{12}\)

\(= 0.75\)

(1) all four units are good is \(P|X = 4| = \frac{\frac 94}{\frac{12}4} = \frac 34\)

(2) Probability of exactly two are good is \(P|X = 2| = \frac{\frac 92}{\frac{12}4} = \frac 32\)

(3) Probability of at least two are good is 

\(P[x \ge 2] = P[X = 2] + P[X = 3] + P[X = 4]\)

\(= \frac{\frac 92}{\frac {12}4} + (\frac 93) (\frac{12}4) + (\frac94) (\frac {12}4)\)

\(= \frac{13}4\)

Comments

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