Answer to Question #286335 in Statistics and Probability for T SID

Question

A flood forecaster issues a flood warning under two conditions only:

i) Winter snowfall exceeds 20 cm, regardless of fall rainfall

ii) Fall rainfall exceeds 10 cm and winter snowfall is between 15 and 20 cm

The probability of winter snowfall exceeding 20cm is 0.05. The probability of winter snowfall of between 15 and 20 cm is 0.10. The probability of fall rainfall exceeding 10 cm is 0.10.

The probability that flooding occurs is 0.75 for condition (i) above, 0.60 for condition (ii) above, and 0.05 for conditions where no flooding was anticipated.

Answer 1

What is the probability that a flood warning will be issued?

Solution:

To find the probability of a flood warning, we multiply probabilities along the branches and sum the ending values for the type (i) and type (ii) warnings.

$P(warning) = (0.05)(1.00) + (0.10)(0.10) = 0.06$