14 Peter wants to pass his driving test. The probability that he passes at his first attempt is 0.7 When Peter passes his driving test, he does not take it again. If he fails, the probability that he passes at the next attempt is 0.8
(a) Complete the probability tree diagram for Peter’s first two attempts.(2)
(b) Calculate the probability that Peter needs exactly two attempts to pass his driving test. (2)
(c) Calculate the probability that Peter passes his driving test at his third or fourth attempt. (3)
Mark scheme (a)
Scheme
Marks
0.3 in first fail branch
B1
0.8, 0.2 in second attempt pass, fail branches
B1
(2)
Notes
B1: Branches must be labelled. Ignore extra branches leading from “pass”.
Mark scheme (b)
Scheme
Marks
“0.3” x 0.8
M1ft
0.24 oe
A1
(2)
Mark scheme (c)
Scheme
Marks
(“0.3” x “0.2” x 0.8) + (“0.3” x “0.2” x “0.2” x 0.8) oe
M2ft
0.0576 oe
A1
(3)
(7 marks)
Notes
M2ft: M1ft for “0.3” x “0.2” x 0.8 (=0.048) or “0.3” x “0.2” x “0.2” x 0.8 (=0.0096)
