7 The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62. The probability that any postcard posted in Portugal on Friday is delivered to the UK within a week is 0.41.
(a) Anna is on holiday in Portugal. She posts 15 postcards to the UK on Monday.
How many of her postcards can she expect to be delivered within a week? [2]
(b) Sergio is in Portugal. He posts one postcard to the UK on Monday. He posts another postcard to the UK on Friday.
(i) Complete the probability tree to show the possible outcomes for the postcards.[2]
(ii) Calculate the probability that only one of Sergio’s postcards is delivered within a week. [3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
9
2
M1 for 15 × 0.62, possibly soi by 9.3
If 0 scored, then SC1 for 15 × 0.41 leading to 6 as final answer
Condone “9 or 10” as final answer for 2 marks if correct working is shown.
Mark scheme (b)
Answer
Marks
Part marks and guidance
(i) Monday: Not delivered within a week 0.38 Friday (on both pairs of branches): Delivered within a week 0.41, Not delivered within a week 0.59
2
B1 for 0.38 and at least one 0.59 seen on correct branches
(ii) 0.5216 or \(\dfrac{326}{625}\)
3
M2FT for (0.62 × their 0.59) + (their 0.38 × 0.41) oe or M1FT for (0.62 × their 0.59) soi by 0.3658 oe or (their 0.38 × 0.41) soi by 0.1558 oe
Condone 0.52 or 0.522 as final answer provided nfww
