Question

The probability that you roll a 5 on a six-sided die is start fraction one over six end fraction . the probability that you flip a coin that lands on heads is start fraction one over two end fraction. the probability that you roll a 5 on a six-sided die and you flip a coin that lands on heads is start fraction one over 12 end fraction. what is the probability of flipping a coin and it landing on heads, given that you rolled a 5 on a six-sided die? are these two events independent?

Answer 1

Let event A be the coin landing on heads and let event B be rolling a 5 on a six-sided die.
Events A and B are independent if, and only if:
$P(A\cap B)=P(A)\times P(B)$
It is given in the question that the above condition for independence is met.
Also A and B are independent if:
P(A|B) = P(A)
P(A) = 1/2
Therefore the probability of flipping a coin and it landing on heads, given that you rolled a 5 on a six-sided die is 1/2. The two events are independent.