(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?
Explanation
(a) (i) No of red discs = (frac{1}{4} times 40 = 10)
Total no of discs = 40
(therefore) No of white balls = 40 – 10 = 30
(ii) Let the number of red balls to be added = z
(therefore frac{10 + z}{40 + z} = frac{1}{3})
(3(10 + z) = 40 + z)
(30 + 3z = 40 + z implies 3z – z = 40 – 30)
(2z = 10 implies z = 5)
Therefore, adding 5 red discs, the probability of picking a red disc = (frac{1}{3}).
(b) CP of a plate = N50.00
Let the number of plates be x
(therefore text{CP of x plates} = N50x)
(text{SP of all plates} = N600)
(frac{100 + 20}{100} times N50x = N600 implies N60x = N600)
(x = frac{600}{60} = 10 plates)