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?

1 Answer
Feb 16, 2016

#20.5%#

Explanation:

Rule of Conditional Probability:
#color(white)("XXX")color(green)(P(a&b)) = color(red)(P(a))xxcolor(blue)(P(b|a))#

Note on notation:
#color(white)("XXX")P(a)#: probability of #a#
#color(white)("XXX")P(a&b)#: probability of both #a# and #b#
#color(white)("XXX")P(b|a)#: probability of #b# given #a#

#color(green)(P("rain" & "hail") = 16%)#
#color(red)(P("rain") = 78%)#

#color(green)(16%) = color(red)(78%) xx color(blue)(P("hail"|"rain"))#

#color(blue)(P("rain"|"hail")) = (color(green)(16%))/(color(red)(78%))~~color(blue)(20.5%)#