"Let's say you flip a coin and roll..." was answered by our community

Craig French

Answered question

2022-02-11

Let's say you flip a coin and roll a die. What is the probability of getting heads and fives?

rossegues03b

Beginner2022-02-12Added 11 answers

Step 1
There are 2 possible outcomes for a coin and 6 for a die.

P (t a i l s) = \frac{1}{2}

(5) = \frac{1}{6}

Since they are independent and we are taliking about an AND -situation we must multiply the probabilities:

\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}

sigcinweq0s

Beginner2022-02-13Added 19 answers

Step 1
First we have to find all possible result of the experiment. If we denote H for heads and T for tails we can write, that:

Ω = {(H, 1); (H, 2); (H, 3); (H, 4); (H, 5); (H, 6); (T, 1); (T, 2); (T, 3); (T, 4); (T, 5); (T, 6)}

So we can see that there are 12 elements in

Ω

. We can write, that:

| Ω | = 12

If we denote A-event of obtaining tails and a five, then we can also write, that:

A = {(T, 50}

, so

| A | = 1

Now we can calculate the probability using the classic definition.

P (A) = \frac{| A |}{| Ω |} = \frac{1}{12}

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