6 randFromArray([4, 6]) randRange(1, GRID_WIDTH) randRange(1, GRID_HEIGHT) randRange(2, GRID_WIDTH + GRID_HEIGHT) (function() { var pairs = [], i, j; for (i = 1; i <= GRID_WIDTH; i++) { for (j = 1; j <= GRID_HEIGHT; j++) { if (PRED(i, j)) { pairs.push([i, j]); } } } return pairs; })() MATCHING_PAIRS.length GRID_WIDTH * GRID_HEIGHT

You are given two dice to roll. One is black with six sides; the other is white with four sides. You are given two six-sided dice to roll.

If it helps, you may select the matching outcomes below. Your selections aren't checked with your answer:

0 of SOLUTION_D selected
Khan.scratchpad.disable(); // Set .e-grid size. $('.e-grid').addClass('e-six-by-' + (GRID_HEIGHT === 6 ? 'six' : 'four')); // Toggle cell selection on click. var selected = $('#e-selected-count'); $('.e-dice').on('click', function() { $(this).toggleClass('e-selected'); selected.text($('.e-selected').length); }); graph.selectMatching = function(matchingPairs) { $(".e-dice").removeClass("e-selected"); _.each(matchingPairs, function(match) { $(".e-dice").eq((match[1] - 1) * 6 + (match[0] - 1)).addClass("e-selected"); }); $("#e-selected-count").text($(".e-selected").length); };
SOLUTION_N / SOLUTION_D

There is one matching outcome.

There are `SOLUTION_N` matching outcomes.

graph.selectMatching(MATCHING_PAIRS);

The probability is the number of matching outcomes divided by all possible outcomes.

The probability is `fraction(SOLUTION_N, SOLUTION_D)`, which reduces to `fractionReduce(SOLUTION_N, SOLUTION_D)`.

The probability is `fractionReduce(SOLUTION_N, SOLUTION_D)`.

function(x, y) { return (x === X && y === Y || x === Y && y === X); }
For a given roll, what is the probability that the dice display `X` and `Y` in any order? For a given roll, what is the probability that the dice display `X` and `Y`? For a given roll, what is the probability that the dice both display `X`?
rand(2) function(x, y) { return x % 2 !== EVEN && y === Y; }
For a given roll, what is the probability that the black die displays an even number and the white die displays `Y`? For a given roll, what is the probability that the black die displays an odd number and the white die displays `Y`?

How many matching outcomes are there with an even number on the black die and `Y` on the white die?

How many matching outcomes are there with an odd number on the black die and `Y` on the white die?

function(x, y) { return x + y === Z; }
For a given roll, what is the probability that the values of the dice add to `Z`?

For each value on the black die, is there a value on the white die that adds to `Z`?

function(x, y) { return x + y <= Z; }
For a given roll, what is the probability that the values of the dice add to `Z` or less?

Count all outcomes that are less than or equal to `Z`.

function(x, y) { return x === y; }
For a given roll, what is the probability you roll the same number on each die?
function(x, y) { return x === X && y === Y; }
For a given roll, what is the probability the black die displays `X` and the white die displays `Y`?
function(x, y) { return x === X || y === X; }
For a given roll, what is the probability at least one die displays `X`?

Remember that both dice can be `X` ("at least one").