19 Kirsty either travels by bus or walks when she visits the shops - OCR - GCSE Maths - Question 18 - 2017 - Paper 1

To find the probability that Kirsty walks at least one way, we can find the probability of her walking both ways and then subtract that from 1 or calculate the individual scenarios in which she walks.

1. Walking to the shops and walking back:

   • The probability of walking to the shops is 0.7
   • The probability of walking back is 0.2

   The combined probability is:

   $P(Walking ext{ both ways}) = 0.7 imes 0.2 = 0.14$

2. Calculate the probability of walking at least one way:
   The probability of NOT walking (i.e. catching the bus both ways) is:

   • Catching the bus to the shops is 0.3
   • Catching the bus back from the shops is 0.8

   Thus, the combined probability of catching the bus both ways is:

   $P(Bus ext{ both ways}) = 0.3 imes 0.8 = 0.24$

3. Final Calculation:
   The probability of walking at least one way is:

   $P(Walking ext{ at least one way}) = 1 - P(Bus ext{ both ways})$
   $= 1 - 0.24 = 0.76$

Thus, the probability that Kirsty walks at least one way is confirmed to be 0.76.