Theory question 106
ProbabilityA bag contains 3 different marbles x, y and z of the same size and shape. The total number of marbles in the bag is 27 and they are such that x : y = 1 : 2 and y : z = 1 : 3
(a) Find the number of z marbles in the bag
(b) Calculate the probability of selecting two of the y marbles at random from the bag one after the other without replacement.
Show the model answer
Model answer
(a) x : y : z = 1 : 2 : 6 (total 9 parts). z = 6/9 × 27 = 18 (and y = 6, x = 3).
(b) P(two y) = 6/27 × 5/26 = 30/702 = 5/117.
Explanation
Combine the two ratios so y has the same number of parts in both.