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, consider both weather conditions, wet and dry:

1. Wet Weather:

   • Probability of wet weather = 0.4
   • Probability of cycling when wet = 0.3

   $P(\text{Cycle | Wet}) = P(\text{Wet}) \times P(\text{Cycle | Wet}) = 0.4 \times 0.3 = 0.12$

2. Dry Weather:

   • Probability of dry weather = 0.6
   • Probability of cycling when dry = 0.8

   $P(\text{Cycle | Dry}) = P(\text{Dry}) \times P(\text{Cycle | Dry}) = 0.6 \times 0.8 = 0.48$

Finally, add the probabilities from both conditions:

$P(\text{Cycle}) = P(\text{Cycle | Wet}) + P(\text{Cycle | Dry})$

Substituting the values:

$P(\text{Cycle}) = 0.12 + 0.48 = 0.60$

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