Theory question 105
ProbabilityA bowl contains red, green and black marbles all of the same size. The number of red marbles are 3 more than the number of green marbles and the number of black marbles is 1 less than the number of green marbles. If the probability of drawing at random a black marble is 1/4, find the: (a) Number of each color of marble (b) Probability that a marble drawn at random from the bowl is not black
Show the model answer
Model answer
(a) Green = g, red = g + 3, black = g − 1; total = 3g + 2
(g − 1)/(3g + 2) = ¼ ⇒ 4g − 4 = 3g + 2 ⇒ g = 6
Green 6, red 9, black 5 (total 20)
(b) P(not black) = 1 − 5/20 = 15/20 = ¾
Explanation
Express every colour in terms of the number of green marbles.