Answer to Question #209753 in Statistics and Probability for Tumelo Makhorole

Question

Assume that a weather forecast for tomorrow states that it rains in Johannesburg with probability 0.2, it rains in pretoria with probability 0.3. Assume further that we are told that if it does rain in pretoria, then it rains in johannesburg with probability 0.8. calculate the probability thatvitvrains in both cities  

Answer 1

$$P(Johannesburg)=0.2, P(Pretoria)=0.3$$

$$P(Johannesburg|Pretoria)=0.8$$

Then

$$P(Johannesburg\cap Pretoria)$$

$$=P(Johannesburg|Pretoria)\cdot P(Pretoria)$$

$$=0.8\cdot0.3=0.24$$

The probability that it rains in both cities  is 0.24.