Neco 2021 Further Mathematics Question 36

Practice objective / multiple choice question 36 from the 2021 Neco Further Mathematics examination.

Neco 2021 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 36 NECO • 2021 • FURTHER_MATHEMATICS • objective

A factory produces two types of widgets: type A (60% of production) and type B (40%). The defect rates are 5% for type A and 12% for type B. Each widget is examined by two independent tests. Test 1 detects a defective widget with probability 0.9 and Test 2 with probability 0.8. A widget that is not detected by either test is said to *pass* both tests.\\n(a) If a widget has passed both tests, find the probability that it is of type A (give your answer to three decimal places).\\n(b) In a batch of 200 widgets, exactly 30 widgets are observed to have passed both tests. Estimate the expected number of defective widgets among those 30 (give your answer to two decimal places).

Answer Options

A. Probability type A ≈ 0.542 (3 d.p.); expected defective ≈ 0.07
Correct Answer B. Probability type A ≈ 0.618 (3 d.p.); expected defective ≈ 0.05
C. Probability type A ≈ 0.600 (3 d.p.); expected defective ≈ 0.12
D. Probability type A ≈ 0.682 (3 d.p.); expected defective ≈ 0.04
Correct Answer
B
Correct Option:
Probability type A ≈ 0.618 (3 d.p.); expected defective ≈ 0.05

About This Question

This is Neco 2021 Further Mathematics Question 36. It is one of the objective questions from the 2021 Neco Further Mathematics examination.

Difficulty level: Hard .

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