$1$
", "$\\displaystyle\\frac{2}{3}$
", "$\\displaystyle\\frac{1}{2}$
", "$\\displaystyle\\frac{1}{3}$
"], "variableReplacements": [], "marks": 0}], "marks": 0, "showFeedbackIcon": true, "variableReplacements": [], "prompt": "What is the probability of rolling an even number?
\n[[0]]
"}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "showCorrectAnswer": true, "gaps": [{"matrix": ["0", "1", 0, 0], "maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", "", "", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "shuffleChoices": false, "showFeedbackIcon": true, "displayColumns": 0, "scripts": {}, "choices": ["$0$
", "$\\displaystyle\\frac{2}{3}$
", "$\\displaystyle\\frac{1}{3}$
", "$\\displaystyle\\frac{1}{4}$
"], "variableReplacements": [], "marks": 0}], "marks": 0, "showFeedbackIcon": true, "variableReplacements": [], "prompt": "What is the probability of not rolling a $\\var{die1}$ or $\\var{die2}$?
\n[[0]]
"}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "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.
"}, "tags": ["taxonomy"], "variables": {"red": {"templateType": "anything", "description": "number of red balls in part c
", "definition": "random(15,19)", "name": "red", "group": "Ungrouped variables"}, "die2": {"templateType": "anything", "description": "Not included number for a) ii)
", "definition": "random(4..6)", "name": "die2", "group": "Ungrouped variables"}, "die1": {"templateType": "anything", "description": "Not included number for a) ii)
", "definition": "random(1..3)", "name": "die1", "group": "Ungrouped variables"}}, "rulesets": {}, "extensions": [], "functions": {}, "ungrouped_variables": ["red", "die1", "die2"], "statement": "You're going to roll a fair six-sided die.
", "advice": "For equally likely outcomes, you can calculate the probability of a particular event occurring by using the formula
\n$\\text{Probability of an event} = \\displaystyle\\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}$.
\nRolling a fair six-sided die has six possible outcomes, each of which is equally likely.
\nLet'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 $1$.
\nHence using the above formula,
\n\\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}
There are three possible outcomes where we roll an even number on the die:
\nUsing the formula for probability for equally likely outcomes, this means that
\n\\[
P(\\text{rolling an even number}) = \\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}= \\frac{3}{6} = \\frac{1}{2}
\\]
To find the probability of not rolling a $\\var{die1}$ or a $\\var{die2}$, we use the same formula again.
\nThe total number of outcomes is still $6$.
\nHere, 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.
\nUsing the formula,
\n\\[
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}
\\]