(a) A box contains 40 identical discs which are either red or white. If the probability of picking a red disc is \(\frac{1}{4}\); Calculate the number of (i...
Question 1 Report
(a) A box contains 40 identical discs which are either red or white. If the probability of picking a red disc is \(\frac{1}{4}\); Calculate the number of (i) white discs ; (ii) red discs that should be added such that the probability of picking a red disc will be \(\frac{1}{3}\).
(b) A salesman bought some plates at N50.00 each. If he sold all of them for N600.00 and made a profit of 20% on the transaction, how many plates did he buy?
Answer Details
(a) Total discs \(= 40\), and \(P(\text{red}) = \dfrac14\), so number of red \(= \dfrac14\times 40 = 10\).
(i) Number of white discs \(= 40 - 10 = 30\).
(ii) Let \(x\) red discs be added. New red count \(= 10 + x\); new total \(= 40 + x\). Require \(P(\text{red}) = \dfrac13\):
\[\frac{10 + x}{40 + x} = \frac13 \;\Rightarrow\; 3(10 + x) = 40 + x \;\Rightarrow\; 30 + 3x = 40 + x\]
\[2x = 10 \;\Rightarrow\; x = 5\]
So \(5\) red discs should be added.
(b) Cost price per plate \(=\) N50. A profit of \(20\%\) on total cost means
\[\text{Selling price} = 1.20 \times \text{Cost price}\]
\[600 = 1.20 \times \text{Cost price} \;\Rightarrow\; \text{Cost price} = \frac{600}{1.20} = \text{N}500\]
\[\text{Number of plates} = \frac{500}{50} = 10\]
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