Question

Determine whether the events are independent or dependent. Then find the probability.A coin is tossed and a die is rolled. What is the probability that the coin lands on hears and the number rolled is greater than 4:

Answer 1

An idependent event is an event that has no connection to another event's chance of happening. In this case since the toss does not affect the roll we have independent events.

Now, the probability of two independent events happening is given by:

`P(A\cap B)=P(A)P(B)`

Let A be the event "The coin lands on heads", in this case we have that the probability is:

`P(A)=(1)/(2)`

Let B the event "The number rolled is grater that 4", in this case we have:

`P(B)=(2)/(6)=(1)/(3)`

Hence the probability of both events happening is:

`P(A\cap B)=(1)/(2)\cdot(1)/(3)=(1)/(6)`

Therefore the probability is 1/6