Subject
Quantitative Aptitude
Topic
Probability
A factory produces four different types of products, P, Q, R and S. The chances that a random piece of products P, Q, R and S is found to be defective are 20%, 30%, 5% and 10%, respectively. During an inspection, one piece of each product is randomly selected. What is the probability that exactly three of them are found to be defective?
A factory produces four different types of products, P, Q, R and S. The chances that a random piece of products P, Q, R and S is found to be defective are 20%, 30%, 5% and 10%, respectively. During an inspection, one piece of each product is randomly selected. What is the probability that exactly three of them are found to be defective?
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0.005খ)
0.0103গ)
0.0124ঘ)
0.0057ঙ)
0.0178Explanation
The chances that a random piece of products P, Q, R and S is found to be defective are 20%, 30%, 5% and 10%, respectively. In terms of probability, this can be stated as probability that a random piece of products P, Q, R and S is found to be defective are 0.20, 0.30, 0.05 and 0.10, respectively. There can be four cases when exactly three of chosen pieces are defective. Case i) Only P, Q and R are defective Probability = 0.2 × 0.3 × 0.05 × (1-0.1) = 0.0027 Case ii) Only P, Q and S are defective Probability = 0.2 × 0.3 × (1-0.05) × 0.1 = 0.0057 Case iii) Only P, R and S are defective Probability = 0.2 × (1-0.3) × 0.05 × 0.1 = 0.0007 Case iv) Only Q, R and S are defective Probability = (1-0.2) × 0.3 × 0.05 × 0.1 = 0.0012 ∴ Probability that exactly three of them are found to be defective = 0.0103Related questions
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