Calculation of conditional probability (hail)

[jones123]

Hi,

If there is a 50% chance of thunderstorms and a 25% chance that if a thunderstorm occurs, it will bring hail, then what is the chance of hail?

Thanks!

 

[Romsek]

$\displaystyle \text{one has to assume some probability for hail if there is no thunderstorm. Once done you can apply}$

$\displaystyle P(H) = P(H|T) P(T) + P(H|!T)P(!T) \\ \text{where $T$ is the event a thunderstorm occurs and $H$ is the event hail occurs}$

 

[jones123]

$\displaystyle \text{one has to assume some probability for hail if there is no thunderstorm. Once done you can apply}$

$\displaystyle P(H) = P(H|T) P(T) + P(H|!T)P(!T) \\ \text{where $T$ is the event a thunderstorm occurs and $H$ is the event hail occurs}$

Obiously, the chance of hail is zero if no thunderstorm occurs. This reduces the equation to:
P(H) = P(H|T) P(T) + P(H|!T)P(!T) = 0.25*0.5 = 0.125

Is that correct?

Thanks!

 

[JeffM]

Well, it is not obvious that hail is caused exclusively by thunderstorms. I had to look up "hail" at wikipedia to confirm that particular meteorological fact. Perhaps you should have posed your question at a help site for meteorologists.

However, given that fact, the second summand in romsek's formula reduces to zero because

[MATH]\text {P(H given not T) * P(not T)} = 0 \text { * P(not T)} = 0.[/MATH]
So you are correct.