The probability of rain and hail during a storm is 16%. The probability of only rain is 78%. What is the probability of hail given that there is already rain?

Question

amistre64 · Answer

when we determine a given; we are looking for the amount of one item that is within the given item.

the intersection of the 2 items is what they have in common, the amount of one that is in the other.  therefore the amount of P(rain and hail) given the P(rain) is what we are looking for.

amistre64 · Answer

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amistre64 · Answer

the P(rain) is [rain only + rain and hail]

given that it is rain, the amount of hail within rain is stated as:  rain and hail

P(rain and hail)
-------------- = P(hail, given that it rains)
     P(rain)