Question

The table gives a set of outcomes and their probabilities. Let A be the event the outcome is prime". Let B be the event "the outcome is less than or equal to 2". Are A and B independent events? Outcome Probability 1 0.1 2 0.1 3 0.3 4 0.2 5 0.3 no yes

Answer 1

A= (the outcome is a prime)

A prime number is a number that is totally divisible by only itself and 1

A = 2,3,5

$\begin{gathered} B\text{ = the outcome is }\leq\text{ 2} \\ B=\text{ 1,2} \end{gathered}$

Since A and B have 2 in common then A and B are not independent events, because independent events are events that can occur without each other. However, A and B Must occur with each other since they have 2 in common