Question

Logan walks his dog every day. They walk by the river 5 days a week and they walk around the block two days a week. When they walk by the river, they see a dog 85% of the time. When they walk around the block, they see other dogs 30% of the time. Determine the probability that Logan and his dog will see another dog on their walk tomorrow. Hint: Draw a tree diagram to represent this situation. (Which way do they walk? Do they see a dog?)

Answer 1

The probabilities of walking tomorrow by the river and the block are 5/7 and 2/7, respectively. On the other hand, the probabilities of seeing another dog by the river and the block are 0.85 and 0.3, respectively.

Therefore,

$P(anotherDog)=\frac{5}{7}\cdot0.85+\frac{2}{7}\cdot0.3=\frac{97}{140}\approx0.693$