WAEC 2012 · Paper 2 · Q4

(a)
A box contains 40 identical discs which are either red or white. If the probability of picking a red disc is $\frac14$ , 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 $\frac13$ .
Separate values with commas, e.g. 3, −2
(b)
A salesman bought some plates at ₦50.00 each. If he sold all of them for ₦600 and made a profit of $20\%$ on the transaction, how many plates did he buy?

Worked solution (try it first)

$P(\text{red}) = \frac{\text{red discs}}{40}$
$= \frac14$ , so there are $\frac14 \times 40 = 10$ red discs and $40 - 10 = 30$ white discs.

Add $r$ red discs.
Then there are $10 + r$ red discs out of $40 + r$ altogether, and we want $\frac{10 + r}{40 + r} = \frac13$ .
Cross-multiply: $3(10 + r) = 40 + r$ , so $30 + 3r = 40 + r$ , $2r = 10$ and $r = 5$ .
Check: $\frac{15}{45} = \frac13$ .