The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62 - OCR - GCSE Maths - Question 7 - 2018 - Paper 6

We start by outlining the possible outcomes for the postcards.

1. For Monday's postcard, there are two outcomes:

   • Delivered within a week (probability = 0.62)
   • Not delivered within a week (probability = 1 - 0.62 = 0.38)

2. For Friday's postcard, the outcomes are:

   • Delivered within a week (probability = 0.41)
   • Not delivered within a week (probability = 1 - 0.41 = 0.59)

The completed probability tree would look like this:

                   Monday's postcard
                   /            \
               Delivered       Not delivered
                 (0.62)              (0.38)
                 /                  \
            Friday's postcard       Friday's postcard
              /          \             /          \
        Delivered     Not delivered  Delivered     Not delivered
        (0.41)          (0.59)      (0.41)      (0.59)

To find the probability that only one of Sergio's postcards is delivered within a week, we consider the following scenarios:

1. Monday's postcard delivered, Friday's postcard not delivered:

   • Probability = $0.62 imes 0.59$

2. Monday's postcard not delivered, Friday's postcard delivered:

   • Probability = $0.38 imes 0.41$

Calculating these:

• For the first scenario:

  $P( ext{M delivered, F not delivered}) = 0.62 imes 0.59 = 0.3658$

• For the second scenario:

  $P( ext{M not delivered, F delivered}) = 0.38 imes 0.41 = 0.1558$

Adding both probabilities gives:

$P( ext{Only one delivered}) = 0.3658 + 0.1558 = 0.5216$

Thus, the probability that only one of Sergio's postcards is delivered within a week is approximately 0.5216.