Probstat/week2 practice 1

This is part of probstat

Conditional probability review

1. Consider a sample space $S=\{0,1,2,3,...,41\}$. We randomly pick an integer from $S$.

1.1 What is the probability that a random number from $S$ is divisible by 2 given that it is divisible by 3.

1.2 Are events "an integer divisible by 2 is picked" and "an integer divisible by 3 is picked" independent?

1.3 What is the probability that a random number from $S$ is divisible by 4 given that it is divisible by 3.

1.4 Are events "an integer divisible by 4 is picked" and "an integer divisible by 3 is picked" independent?