[Math] Whether Wednesday Will Rain. (Homework)

probability

The probability that Monday is wet is 0.4, so the probability of it not raining is 0.6. If there is one day being wet the chance of the next day being wet is 0.2. However, if one day is fine (not wet) the probability the next day will be fine is 0.7.
If Monday is fine, calculate the probability that Wednesday is fine (same week).

I tried doing:(F being Fine, $\ F_m $ being Monday is fine)
$\ (F_m\bigcap\ F\bigcap F)\ $
Which is: $\ 0.6*0.7*0.7 = 0.294 $ Which is wrong. Is there any other ways of approaching this? Thanks in advance.

Best Answer

Split it into $\color\red{\text{disjoint}}$ events, and then add up their probabilities:

  • The probability that Tuesday is $\color\red{\text{dry}}$ and Wednesday is dry is $\color\red{0.7}\cdot0.7=0.49$
  • The probability that Tuesday is $\color\red{\text{wet}}$ and Wednesday is dry is $(\color\red{1-0.7})\cdot(1-0.2)=0.24$

Hence the probability that Wednesday is dry is $0.49+0.24=0.73$.

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