Question

Question 3

(Score for Question 3: _of 6 points)
3. In a game, if you roll a 6 on a 6-sided number cube, you lose a turn.
(a) What is the probability that you roll a 6? Explain your reasoning.
(b) What is the probability that you either roll a 6 or do not roll a 6? Explain your reasoning.
(c) What is the probability that you don't roll a 6? Explain your reasoning.
Answer.​

Answer 1

(a) What is the probability that you roll a 6?

1/6

(b) What is the probability that you either roll a 6 or do not roll a 6?

1

(c) What is the probability that you don't roll a 6?

5/6

Explanation:

(a) What is the probability that you roll a 6?

In a 6- sided cube, a 6 occurs only once. That is only one face is labelled 6. Therefore, the probability that you roll a 6 is;

(number of faces labelled 6)/(totals number of sides) = 1/6

(b) What is the probability that you either roll a 6 or do not roll a 6?

The probability of rolling a 6 was found to be, 1/6.

On the other hand, the probability of not rolling a 6 is;

(number of faces not labelled 6)/(totals number of sides) = 5/6

Therefore, the probability that you either roll a 6 or do not roll a 6 is;

1/6 + 5/6 = 1

These two events are mutually exclusive and exhaustive.

(c) What is the probability that you don't roll a 6?

The probability of not rolling a 6 is;

(number of faces not labelled 6)/(totals number of sides) = 5/6

We have 5 faces not labelled 6 out of 6 possible faces or outcomes