If it rains tomorrow the probabliity is .8 that John will practice his piano lesson. IF it does not rain tomorrow, there is only a .4 chance that John will practice. Suppose that the chance of rain tomorrow is 60%. What is the probablility that John will practice his pianio lessons?
rain and practice ==> (.60)(.80) = .48
no rain and practice ==> (.40)(.40) = .16
add these to get: .64
there is a probability of .64 that John will practice
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as a check:
rain and no practice: (.60)(.20) = .12
no rain and no practice (.40)(.60) = .24
.12 + .24 = .36 = P(no practice)
P(practice) + P(no practice) = .64 + .36 = 1 yep, it works