randFromArray(["bag", "jar", "box", "cup"]) randFromArray(["marble", "ball", "jelly bean"]) randRange(3, 11) randRange(3, 11) randRange(3, 11) RED + GREEN + BLUE rand(2) == 0 randFromArray([["red", RED], ["green", GREEN], ["blue", BLUE]]) NOT ? TOTAL - CHOSEN_NUMBER : CHOSEN_NUMBER

A CONTAINER contains RED red MARBLEs, GREEN green MARBLEs, and BLUE blue MARBLEs.

If a MARBLE is randomly chosen, what is the probability that it is not CHOSEN_COLOR? Write your answer as a simplified fraction.

NUMBER / TOTAL

There are RED + GREEN + BLUE = TOTAL MARBLEs in the CONTAINER.

There are CHOSEN_NUMBER CHOSEN_COLOR MARBLEs. That means TOTAL - CHOSEN_NUMBER = NUMBER are not CHOSEN_COLOR.

The probability is \displaystyle fractionSimplification(NUMBER, TOTAL).

randFromArray([ ["a 1", [1]], ["a 2", [2]], ["a 3", [3]], ["a 4", [4]], ["a 5", [5]], ["a 6", [6]], ["at least 2", [2, 3, 4, 5, 6]], ["at least 3", [3, 4, 5, 6]], ["at least 4", [4, 5, 6]], ["more than 2", [3, 4, 5, 6]], ["more than 3", [4, 5, 6]], ["more than 4", [5, 6]], ["less than 4", [1, 2, 3]], ["less than 5", [1, 2, 3, 4]], ["less than 6", [1, 2, 3, 4, 5]], ["even", [2, 4, 6]], ["even", [2, 4, 6]], ["odd", [1, 3, 5]], ["odd", [1, 3, 5]], ["prime", [2, 3, 5]] ]) RESULT_POSSIBLE.length

A fair six-sided die is rolled. What is the probability that the result is RESULT_DESC? Write your answer as a simplified fraction.

RESULT_COUNT / 6

When rolling a die, there are 6 possibilities: 1, 2, 3, 4, 5, and 6.

In this case, only 1 result is favorable: the number RESULT_POSSIBLE[0].

In this case, RESULT_COUNT results are favorable: toSentence(RESULT_POSSIBLE).

The probability is \displaystyle fractionSimplification(RESULT_COUNT, 6).

randFromArray([ [3, "no heads", [0]], [3, "heads exactly once", [1]], [3, "heads exactly twice", [2]], [3, "heads at least once", [1, 2, 3]], [3, "heads at least twice", [2, 3]], [3, "heads every time", [3]], [4, "no heads", [0]], [4, "heads exactly once", [1]], [4, "heads exactly twice", [2]], [4, "exactly three heads", [3]], [4, "heads at least once", [1, 2, 3, 4]], [4, "heads at least twice", [2, 3, 4]], [4, "at least three heads", [3, 4]], [4, "heads every time", [4]], [3, "no tails", [3]], [3, "tails exactly once", [2]], [3, "tails exactly twice", [1]], [3, "tails at least once", [0, 1, 2]], [3, "tails at least twice", [0, 1]], [3, "tails every time", [0]], [4, "no tails", [4]], [4, "tails exactly once", [3]], [4, "tails exactly twice", [2]], [4, "exactly three tails", [1]], [4, "tails at least once", [0, 1, 2, 3]], [4, "tails at least twice", [0, 1, 2]], [4, "at least three tails", [0, 1]], [4, "tails every time", [0]] ]) coinFlips(REPS) (function() { return jQuery.map(ALL, function( el, i ) { return el[0]; }); })() (function() { return jQuery.map(jQuery.grep(ALL, function( el, i ) { return WANTED.indexOf(el[1]) !== -1; }), function( el, i ) { return el[0]; }); })() choose(REPS, WANTED) pow(2, REPS)

A fair coin is flipped REPS == 3 ? "three" : "four" times. What is the probability of getting DESC? Write your answer as a simplified fraction.

WANTED_COUNT / TWO_TO_REPS

There are (new Array(REPS)).join("2 \\cdot ")2 = 2^{REPS} = TWO_TO_REPS possibilities for the sequence of flips.

The possibilities are toSentence(ALL_SEQS).

There WANTED_COUNT == 1 ? "is only" : "are" plural(WANTED_COUNT, "favorable outcome"): toSentence(WANTED_LIST).

The probability is \displaystyle fractionSimplification(WANTED_COUNT, TWO_TO_REPS).

randFromArray([ [1, 10], [11, 20], [21, 30], [31, 40], [41, 50], [51, 60], [61, 70], [71, 80], [81, 90], [91, 100] ]) (function() { var list = []; for (var i = LOW; i <= HIGH; i++) { list.push(i); } return list; })() randFromArray([ ["prime", KhanUtil.isPrime], ["divisible by both 2 and 3", function(n) { return n % 6 <= 0.5; }], ["divisible by either 3 or 5", function(n) { return n % 3 <= 0.5 || n % 5 <= 0.5; }], ["divisible by either 4 or 7", function(n) { return n % 4 <= 0.5 || n % 7 <= 0.5; }] ]) jQuery.grep(POSSIBLE, COND_FN) WANTED_LIST.length

A positive integer is picked randomly from LOW to HIGH, inclusive.

What is the probability that it is COND_DESC? Write your answer as a simplified fraction.

WANTED_COUNT / POSSIBLE.length

There are POSSIBLE.length possibilities for the chosen number.
The possibilities are toSentence(POSSIBLE).

There WANTED_COUNT == 1 ? "is only" : "are" plural(WANTED_COUNT, "favorable outcome"): toSentence(WANTED_LIST).

The probability is \displaystyle fractionSimplification(WANTED_COUNT, POSSIBLE.length).