The probability that Adam cycles to school or walks to school depends on the weather - OCR - GCSE Maths - Question 23 - 2020 - Paper 3

To find the total probability that Adam cycles to school, we consider both scenarios: when the weather is wet and when it is dry.

1. Wet Weather:

   • Probability of wet weather: $P(Wet) = 0.4$
   • Probability of cycling when wet: $P(Cycle | Wet) = 0.3$
   • Joint probability for wet:
     $P(Wet ext{ and } Cycle) = P(Wet) imes P(Cycle | Wet) = 0.4 imes 0.3 = 0.12$

2. Dry Weather:

   • Probability of dry weather: $P(Dry) = 0.6$
   • Probability of cycling when dry: $P(Cycle | Dry) = 0.8$
   • Joint probability for dry:
     $P(Dry ext{ and } Cycle) = P(Dry) imes P(Cycle | Dry) = 0.6 imes 0.8 = 0.48$

Finally, sum the probabilities from both scenarios: $P(Cycle) = P(Wet ext{ and } Cycle) + P(Dry ext{ and } Cycle) = 0.12 + 0.48 = 0.60$

Therefore, the probability that Adam cycles to school is 0.60.