The management believes that the weather conditions significantly impact the level of demand and the estimated probabilities of poor weather conditions given different levels of demand is presented below. $\text { P (Poor } \mid \text { High } ) = .2 , \text { P(Poor } \mid \text { Medium } ) = .5 , \text { P } ( \text { Poor } \mid \text { Low } ) = .8$
P(High) = 15/48,P(Medium) = 28/48,P(Low) = 5/48
What is the probability of high demand given that the weather conditions are poor?

Question

The management believes that the weather conditions significantly impact the level of demand and the estimated probabilities of poor weather conditions given different levels of demand is presented below.

\text { P (Poor } \mid \text { High } ) = .2 , \text { P(Poor } \mid \text { Medium } ) = .5 , \text { P } ( \text { Poor } \mid \text { Low } ) = .8

P(High) = 15/48,P(Medium) = 28/48,P(Low) = 5/48
What is the probability of high demand given that the weather conditions are poor?

Quizplus · Accepted Answer

To find the probability of high demand given poor weather conditions, we use Bayes' theorem. The formula for Bayes' theorem in this context is $$P(\text{High} | \text{Poor}) = \frac{P(\text{Poor} | \text{High}) \times P(\text{High})}{P(\text{Poor})}$$. We already have $P(\text{Poor} | \text{High}) = 0.2$ and $P(\text{High}) = 15/48$. To find $P(\text{Poor})$, we calculate it as $P(\text{Poor}) = P(\text{Poor} | \text{High}) \times P(\text{High}) + P(\text{Poor} | \text{Medium}) \times P(\text{Medium}) + P(\text{Poor} | \text{Low}) \times P(\text{Low})$, which gives us $P(\text{Poor}) = 0.2 \times 15/48 + 0.5 \times 28/48 + 0.8 \times 5/48$. Substituting these values into Bayes' theorem gives us the probability of high demand given poor weather conditions, which is approximately 0.1429 or 14/29.

The Management Believes That the Weather Conditions Significantly Impact the Level