Answer:
a. x is 55
b. 20 white marbles
Explanation:
Question: A box contains 60 identical marbles where 'x' of them are red while the rest are white; (given that in the original question, the box only contains red and yellow marbles, the yellow can be replaced by white to explain the question idea)
a. The number of identical marbles in the box, n = 60
The number of red marbles = x
The number of white marbles = The rest of the marbles which are not red
The probability that a marble drawn is white, P(y) = 1/12
Let 'y' represent the number of white marbles
From probability theory, we have;
The number of white marbles, y = n × P(y) = 60 × 1/12 = 5
The number of red marbles, x = n - y = 60 - 5 = 55
x = 55
b. The number of white marbles that must be added to make the probability of choosing a white marble = 5/16 is given as follows;
Let Δy represent the number of white marbles added, therefore;
P(y) = (y + Δy)/(y + Δy + x)
∴ P(y) = (5 + Δy)/(5 + Δy + 55) = 5/16
5 × (60 + Δy) = 16 × (5 + Δy)
300 + 5·Δy = 80 + 16·Δy
16·Δy - 5·Δy = 300 - 80
11·Δy = 220
Δy = 220/11 = 20
The number of white marbles that must be added, Δy = 20 white marbles