12 In a computer game the player can either win or lose. A student thinks the ratio of the probability of winning to the probability of losing is 2 : 3. The student plays two games.
(a) Use the information to complete the tree diagram.
[3]
(b) Find the probability that the student wins at least one of the two games. [3]
(c) The student now thinks the ratio of the probability of winning to the probability of losing has changed to 2 : 5.
Explain the effect this change will have on your answer to part (b). [1]
Mark scheme (a)
Answer
Marks
Part marks and guidance
0.4 and 0.6 oe on the correct branches
3
B1 for 0.4 or 0.6 oe M1 for 0.4 and 0.6 on first branch or on all second branches in the correct places If 0 scored SC1 for two probabilities consistently placed and adding to 1
Accept equivalent fractions \(\frac{2}{5}\) and \(\frac{3}{5}\)
Mark scheme (b)
Answer
Marks
Part marks and guidance
0.64 or \(\frac{16}{25}\) oe
3
FT for M1 and M2 and 3 from their 0.6 and their 0.4 throughout providing their 0.6 + their 0.4 = 1 M2 for correct method e.g. 1 – their 0.6 × their 0.6 oe or M1 for one correct branch e.g. their 0.6 × their 0.6 or their 0.4 × their 0.6
Accept 64% for 3 marks
e.g. M2 for their \(\frac{2}{5}\) + their \(\frac{3}{5}\) × their \(\frac{2}{5}\)
for one correct branch condone just P(win) e.g. their \(\frac{2}{5}\)
Mark scheme (c)
Answer
Marks
Part marks and guidance
any correct reason e.g. the answer will be smaller
1
Their answer should explain the effect on the answer to part (b), ignore calculations, see appendix
Appendix: exemplar responses for Q12(c)
Response
Mark
[the answer] it will be smaller
1
the probability of winning will decrease
1bod
The probability of losing will increase
1 bod
They win less games
0
the answer will change because the probabilities have changed
