The probability that it will rain tomorrow is \(\frac{5}{8}\).
If it rains, the probability that Rafael walks to school is \(\frac{1}{6}\).
If it does not rain, the probability that Rafael walks to school is \(\frac{7}{10}\).
(a) Complete the tree diagram.
(b) Calculate the probability that it will rain tomorrow and Rafael walks to school.
(c) Calculate the probability that Rafael does not walk to school.
▶️ Answer/Explanation
(a) Ans: \(\frac{5}{8}\), \(\frac{3}{8}\), \(\frac{1}{6}\), \(\frac{5}{6}\), \(\frac{7}{10}\), \(\frac{3}{10}\)
First branch: Rain (\(\frac{5}{8}\)) and No Rain (\(\frac{3}{8}\)).
Second branch (Rain): Walk (\(\frac{1}{6}\)) and No Walk (\(\frac{5}{6}\)).
Second branch (No Rain): Walk (\(\frac{7}{10}\)) and No Walk (\(\frac{3}{10}\)).
(b) Ans: \(\frac{5}{48}\)
Multiply the probabilities: \(P(\text{Rain}) \times P(\text{Walk}|\text{Rain}) = \frac{5}{8} \times \frac{1}{6} = \frac{5}{48}\).
(c) Ans: \(\frac{304}{480}\) (or simplified \(\frac{19}{30}\))
Calculate \(P(\text{No Walk}|\text{Rain}) = \frac{5}{8} \times \frac{5}{6} = \frac{25}{48}\).
Calculate \(P(\text{No Walk}|\text{No Rain}) = \frac{3}{8} \times \frac{3}{10} = \frac{9}{80}\).
Add them: \(\frac{25}{48} + \frac{9}{80} = \frac{125}{240} + \frac{27}{240} = \frac{152}{240} = \frac{304}{480}\).