In a village, if it rains on one day, the probability that it will rain on the next day is 0.8 if it does not rain on one day, the probability that it will rain on the next day is 0.6 A weather forecaster says, "There is a 70% chance that it will rain in the village on Monday." Work out an estimate for the probability that it will rain in the village on Wednesday - Edexcel - GCSE Maths - Question 21 - 2021 - Paper 2

The probability of rain on Tuesday given that it does not rain on Monday is 0.6. Therefore:

$P(Raining ext{ on Tuesday} | Not Raining ext{ on Monday}) = 0.6$.

Using the law of total probability, the probability of raining on Wednesday can be calculated:

Let:

• $P(R_{M}) = 0.7$ (Probability of rain on Monday)
• $P(N_{M}) = 0.3$ (Probability of no rain on Monday)

Using these, we have:

$P(R_{W}) = P(R_{W} | R_{T}) imes P(R_{T}) + P(R_{W} | N_{T}) imes P(N_{T})$ Where:

• $P(R_{W} | R_{T}) = 0.8 \times 0.7 = 0.56$
• $P(R_{W} | N_{T}) = 0.6 \times 0.3 = 0.18$

So, $P(R_{W}) = 0.56 + 0.18 = 0.74$.

Therefore, the estimated probability that it will rain in the village on Wednesday is:

$0.74$.