// Numbas version: finer_feedback_settings {"name": "Choose the probability of getting certain scores on a die", "extensions": [], "custom_part_types": [], "resources": [["question-resources/dice.svg", "/srv/numbas/media/question-resources/dice.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "

First part asks for the probability of rolling an even number. Second part asks for the probability of not rolling either of two given numbers.

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For equally likely outcomes, you can calculate the probability of a particular event occurring by using the formula

$\\text{Probability of an event} = \\displaystyle\\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}$.

Rolling a fair six-sided die has six possible outcomes, each of which is equally likely.

Let's say we want to find the probability of rolling a $2$. There is only one outcome which involves a $2$ being rolled, so the number of favourable outcomes is $1$.

Hence using the above formula,

\\begin{align}
P(\\text{rolling a $2$}) &= \\displaystyle\\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}\\\\
&= \\displaystyle\\frac{1}{6}
\\end{align}

a)

There are three possible outcomes where we roll an even number on the die:

we roll a $2$;
we roll a $4$;
we roll a $6$.

Using the formula for probability for equally likely outcomes, this means that

\\[
P(\\text{rolling an even number}) = \\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}= \\frac{3}{6} = \\frac{1}{2}
\\]

b)

To find the probability of not rolling a $\\var{die1}$ or a $\\var{die2}$, we use the same formula again.

The total number of outcomes is still $6$.

Here, we have four possible outcomes which don't involve rolling a $\\var{die1}$ or a $\\var{die2}$, i.e. when we roll any of the other numbers on the die.

Using the formula,

\\[
P(\\text{not rolling a $\\var{die1}$ or a $\\var{die2}$}) = \\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}} = \\frac{4}{6} = \\frac{2}{3}
\\]

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Not included number for a) ii)

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number of red balls in part c

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Not included number for a) ii)

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You're going to roll a fair six-sided die.

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What is the probability of rolling an even number?

[[0]]

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$1$

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$\\displaystyle\\frac{2}{3}$

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$\\displaystyle\\frac{1}{2}$

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$\\displaystyle\\frac{1}{3}$

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What is the probability of not rolling a $\\var{die1}$ or $\\var{die2}$?

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$0$

", "

$\\displaystyle\\frac{2}{3}$

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$\\displaystyle\\frac{1}{3}$

", "

$\\displaystyle\\frac{1}{4}$

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