NECO 2023 · Paper 2 · Q14

(a)
A fair coin is tossed four times. Calculate the probability of obtaining (i) at least one tail; (ii) an equal number of heads and tails.
Separate values with commas, e.g. 3, −2
(b)
The annual demand for a product is 800 units and the unit price is ₦2.00. If the ordering cost is ₦5.00 and the holding cost is $10\%$ of the unit price, calculate the total variable cost per annum (₦).

Worked solution (try it first)

(a)(i)

At least one tail is everything except four heads: $1 - \left(\frac12\right)^4 = \frac{15}{16}$ .

(ii)

Two heads and two tails: $\binom42\left(\frac12\right)^4 = \frac{6}{16}$
$= \frac38$ .

(b)

The holding cost per unit is $10\%$ of ₦2.00, which is ₦0.20.
The economic order quantity is $\sqrt{\dfrac{2 \times 800 \times 5}{0.2}} = \sqrt{40\,000}$
$= 200$ units.
Ordering cost: $\dfrac{800}{200} \times 5 = ₦20$ .
Holding cost: $\dfrac{200}{2} \times 0.20 = ₦20$ .
Total variable cost: $₦20 + ₦20 = ₦40.00$ per annum.

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