Coin Flipped, Dice Rolled Probability What is the probability of a tail and a 3? I really struggle with probability so I was wondering if anyone could explain it clearly so that I can learn it for future.
 A: So Suppose you first coined toss only possible outcomes are Heads(H) or Tails.
Then you rolled dice you get no. between 1,2,3,4,5,6.
So, your sample space is what is your possible outcomes are.
But, you don't know whether you get heads or tails; also you don't know whether you got which number between 1 to 6.
So, you write sample space as {H1, H2,......H6, T1, T2,...T6}
where H1 is you got head and got 1 on dice and similarly all others.
Probability is just like chance so you got Tail and 3 is one of the outcomes of sample space and there are 12 possible outcomes out of which only certain can happen depending on what question type.
SO, probability of getting tail and 3 is 1/12
A: The probability of a tail is $\frac12$ since there are two possibilities to choose from: heads and tails. The probability of a $3$ is $\frac16$ because there are six possibilities to choose from: $1, 2, \dots, 6$. The two events are independent. Thus the probability of them both happening is $$\frac12\times\frac16=\frac{1}{12}.$$
Another way to look at it is that there are twelve pairs $H1, H2, \dots , H6, T1, T2, \dots, T6$ in your sample space and you choose one of them.
