$2$ Dice are rolled, 1 red and 1 blue.

Question

$2$ Dice are rolled, $1$ red and $1$ blue. What is the probability of rolling a 6 on the red or blue dice?

Options.
1: $1/6$
2: $1/36$
3: $11/36$
4: $2/6$

Answer 1

A will be the probability of 6 on the red and B will be the probability of 6 on the blue one.

A U B \ A * B Result: 1/ 6 + 1/6 - 1/ 36= 11/36

Answer 2

Using counterprobabilities, one obtains $$1-\underbrace{((\underbrace{1-\frac{1}{6}}_{\text{prob. of not rolling a }6\text{ with red die }})(\underbrace{1-\frac{1}{6}}_{\text{prob. of not rolling a }6\text{ with blue die }}))}_{\text{prob. of not rolling a $6$ with any die}}=\frac{11}{36}.$$

Answer 3

By the statement "Rolling a $6$ on the red or the blue", we mean that after rolling the dice, 6 turns up either on the red die or on the blue die or both.

Now, from the sample space of $36$ possible outcomes, only one outcome is of getting a $6$ on both the dice.

Total outcomes where $6$ is rolled on the red die only are $5$ and so are for the blue die.

Thus, the probability that the statement given occurs is $\dfrac{1}{36} + \dfrac{5}{36} + \dfrac{5}{36} = \dfrac{11}{36}$. Thus, option (c) is correct.

Answer 4

Rolling two dices gives you $36$ couples on which $(6,6)$, $(6,*)$ (i.e. $(6,5)$,$(6,4)$, etc...), $(*,6)$ (i.e. $(5,6)$,$(4,6)$, etc...) so $11$ couples, corresponding to one of the dices rolling a 6. So the answer is 11/36.