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:

F - 5 on a six-sided die,
H - coin lands on heads

We also know that:


`P(F)=(1)/(6)\qquad\qquad P(H)=(1)/(2)\qquad\qquad P(F\cap H)=(1)/(12)`

Calculate:


`P(H|F)=(P(F\cap H))/(P(F))=((1)/(12))/((1)/(6))=(1\cdot6)/(12\cdot1)=(6)/(12)=\boxed{(1)/(2)}`

In this case events are independent when:


`P(H|F)=P(H)`

Both probabilities equals
`(1)/(2)`, so H and F are independent.

Answer 2

I am not sure about the probability but I cant tell you these events are independent because u don't need to roll a five for a coin to land on heads