16 The probability that it will rain on Saturday is 0.8
If it rains on Saturday, the probability that it will rain on Sunday is 0.65 If it does not rain on Saturday, the probability that it will rain on Sunday is 0.4
(a) Use this information to complete the probability tree diagram.(2)
(b) Work out the probability that it will rain on just one of these two days. (3)
Mark scheme (a)
Scheme
Marks
0.2, 0.65, 0.35, 0.4, 0.6
B2oe
(2)
Notes
B2oe: B1 for any 2 correct probabilities (in correct position)
Mark scheme (b)
Scheme
Marks
0.8 × “0.35”(=0.28) or “0.2” × “0.4”(=0.08)
M1
0.8 × “0.35” + “0.2” × “0.4”
M1
0.36 oe
A1
(3)
(5 marks)
Notes
M1: ft from (a)
M1: ft from (a)
A1: eg \(\dfrac{9}{25}\), 36%
M2 ft from (a) for 1 – (0.8 × ‘0.65’ + ‘0.2’ × ‘0.6’) M1 for 1 – (0.8 × ‘0.65’) or 1 – (‘0.2’ × ‘0.6’)
(corrected from the printed mark scheme: 1 – (0.8 × ‘0.6’ + ‘0.2’ × ‘0.6’))
