Gce Model Questions Vol1 2025 Further Mathematics Question 35

Practice objective / multiple choice question 35 from the 2025 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2025 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 35 GCE_MODEL_QUESTIONS_VOL1 • 2025 • FURTHER_MATHEMATICS • objective

A factory uses two machines, \(M_{1}\) and \(M_{2}\), to produce widgets. Machine \(M_{1}\) supplies \(60\%\) of the output and its defect rate is \(2\%\); machine \(M_{2}\) supplies \(40\%\) of the output and its defect rate is \(5\%\). From a day's production a quality‑control inspector selects five widgets at random (the total production is large enough to treat the selections as independent).\n\n(a) What is the probability that exactly two of the five selected widgets are defective, given that at least one is defective?\n(b) What is the expected number of defective widgets in the sample of five?

Answer Options

A. (a) \(\displaystyle \frac{10\left(\frac{4}{125}\right)^{2}\left(\frac{121}{125}\right)^{3}}{1-\left(\frac{121}{125}\right)^{5}}\approx 0.058\). (b) Expected value \(=0.20\).
Correct Answer B. (a) \(\displaystyle \frac{10\left(\frac{4}{125}\right)^{2}\left(\frac{121}{125}\right)^{3}}{1-\left(\frac{121}{125}\right)^{5}}\approx 0.062\). (b) Expected value \(=0.16\).
C. (a) \(\displaystyle \frac{5\left(\frac{4}{125}\right)^{2}\left(\frac{121}{125}\right)^{3}}{1-\left(\frac{121}{125}\right)^{5}}\approx 0.031\). (b) Expected value \(=0.12\).
D. (a) \(\displaystyle \frac{10\left(\frac{4}{125}\right)^{1}\left(\frac{121}{125}\right)^{4}}{1-\left(\frac{121}{125}\right)^{5}}\approx 0.045\). (b) Expected value \(=0.18\).
Correct Answer
B
Correct Option:
(a) \(\displaystyle \frac{10\left(\frac{4}{125}\right)^{2}\left(\frac{121}{125}\right)^{3}}{1-\left(\frac{121}{125}\right)^{5}}\approx 0.062\). (b) Expected value \(=0.16\).

About This Question

This is Gce Model Questions Vol1 2025 Further Mathematics Question 35. It is one of the objective questions from the 2025 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Hard .

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