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You roll a 6 sided die. What is p(6 or even)? Simplified your answer and write it as a fraction or whole number.

You roll a 6-sided die.

I am working on this. Thanks for having me.

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    What attempts have you made on the problem? Where are you getting stuck? – 2017-02-22
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    What have you tried? Write the scenario out and think about the outcomes as a set. – 2017-02-22
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    For extra points: what is $P(37$ or even$)$? – 2017-02-22

3 Answers 3

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Because all outcomes are equally weighted, the probability you are looking for is given by :- $$\frac{\text{Number of favorable events}}{\text{Total number of events}}$$

In your case: $6\text{ or Even outcome}=\{2,4,6\}$ and $\text{Outcomes}=\{1,2,3,4,5,6\}$

Hence:

$$\frac{\text{Number of favourable events}}{\text{Total number of events}}=\frac{3}{6}=\frac1{2}$$

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    Why downvote plz? – 2017-02-22
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You can find the probablity of the desired event not happening, and then subtracting $1$ from that. The only ways that you could not roll $6$ or even are $1$, $3$, and $5$ so $\frac 36$ of your outcomes. Now we subtract $1$ to get the $P(6$ or even$)$ $$1-\frac 36=\frac 36=\frac 12$$

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    The events $6$ and $Even$ are not independent... you cannot added them up – 2017-02-22
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    Ahh yes elementary mistake. I adjusted my approach to get the right answer. – 2017-02-22
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    Looking at complements is over complicating the issue. Just observe directly that $\mathsf P\underbrace{(\{6\}\cup\{2,4,6\})}_{''6\text{ or even}''}~=~\mathsf P(\{2,4,6\})$ – 2017-02-22
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Since the outcome that the dice rolls a 6 is included in the 2nd outcome that the dice rolls an even, the answer is the probability of the 2nd outcome, or an even roll on the dice.

Long winded math explanation: The probability of outcome 1 OR outcome 2 is:

((chance of outcome 1) + (chance of outcome 2) - chance of outcome 1 AND 2)

The probability of rolling just a 6 is $\frac{1}{6}$. The probability of rolling an even number is $\frac{1}{2}$. The probability of rolling an even number that is a 6 is $\frac{1}{6}$.

So, putting this into the above mentioned formula, $(\frac{1}{6} + \frac{1}{2}) - \frac{1}{6} = \frac{1}{2}$.

Which is the probability of event 2, or rolling an even number. Hope this helps!