EconOcon is planning its company picnic. The only thing that will canc

Schwelliney

Schwelliney

Answered question

2021-11-13

EconOcon is planning its company picnic. The only thing that will cancel the picnic is a thunderstorm. The Weather Service has predicted dry conditions with probability 0.2, moist conditions with probability 0.45, and wet conditions with probability 0.35. If the probability of a thunderstorm given dry conditions is 0.3, given moist conditions is 0.6, and given wet conditions is 0.8, what is the probability of a thunderstorm? If we know the picnic was indeed canceled, what is the probability moist conditions were in effect?

Answer & Explanation

Greg Snyder

Greg Snyder

Beginner2021-11-14Added 11 answers

Step 1
Let D represent the weather service has predicted dry condition and P(D)=0.2
M represent moist condition and P(M)=0.45
W represent wet condition and P(W)=0.35
Let T be the event for thunderstorm.
and P(TD)=0.3
P(TM)=0.6
P(TW)=0.8
Step 2
We have to find the probability of a thunderstorm as
P(T)=P(TD).P(D)+P(TM).P(M)+P(TW).P(W)
=0.30.2+0.60.45+0.80.35
=0.06+0.27+0.28
P(T)=0.61
The probability of a thunderstorm is 0.61.
Step 3
We have to find the probability of moist conditions were in effect as.
P(MT)=P(TM).P(M)P(T)
P(MT)=0.60.450.61
P(MT)=0.270.61
P(MT)=0.4426
If we know the picnic was indeed cancelled the probability moist conditions were effect is 0.4426.

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