16 A bag contains 3 white discs and 1 black disc. John takes at random 2 discs from the bag without replacement.
(a) Complete the probability tree diagram.(3)
(b) Find the probability that both discs are white. (2)
(c) All the discs are now replaced in the bag. Pradeep takes at random 3 discs from the bag without replacement. Find the probability that the disc left in the bag is white. (3)
Mark scheme (a)
Scheme
Marks
\(\frac{1}{4}\) on Black branch
B1
Correct tree structure
B1
Labels and values correct
B1
(3)
Notes
B1:
Mark scheme (b)
Scheme
Marks
\(\frac{3}{4} \times \frac{2}{3}\)
M1 ft
\(\frac{1}{2}\)
A1
(2)
Notes
M1 ft: Allow ft if ww selected from tree diagram or \(\frac{3}{4} \times \frac{3}{4}\)
A1: cao
Mark scheme (c)
Scheme
Marks
\(\frac{3}{4} \times \frac{2}{3} \times \frac{1}{2}\) or \(\frac{3}{4} \times \frac{1}{3}\) or \(\frac{1}{4}\)
