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Probability

Probability is about how Likely something is to occur, or how likely something is true.

The mathematic probability is a Number between 0 and 1.

0 indicates Impossibility and 1 indicates Certainty.

The Probability of an Event

The probability of an event is:

The number of ways the event can happen / The number of possible outcomes.

Probability = # of Ways / Outcomes


Tossing Coins

Coin Coin

When tossing a coin, there are two possible outcomes:

WayProbability
Heads1/2 = 0.5
Tails1/2 = 0.5

P(A) - The Probability

The probability of an event A is often written as P(A).

When tossing two coins, there are 4 possible outcomes:

EventP(A)
Heads + Heads1/4 = 0.25
Tails + Tails1/4 = 0.25
Heads + Tails1/4 = 0.25
Tails + Heads1/4 = 0.25

Throwing Dices

Dice Dice Dice

When throwing a dice, there are 6 possible outcomes:

EventP(A)
Lands on 11/6 = 0.166666
Lands on 21/6 = 0.166666
Lands on 31/6 = 0.166666
Lands on 41/6 = 0.166666
Lands on 51/6 = 0.166666
Lands on 61/6 = 0.166666

The possibility of throwing 3 fours at the same time is
(1/6)3 (Lands on 4 to the power of 3):

The possibility is:

let p = Math.pow(1/6, 3);

Try it Yourself »

The possibility of throwing 3 likes at the same time is 6 times larger:
(lands on 1) + (Lands on 2) + ... + (Lands on 6)

The possibility is:

let p = Math.pow(1/6, 3) * 6;

Try it Yourself »



6 Balls

I have 6 balls in a bag: 3 reds, 2 are green, and 1 is blue.

Blindfolded. What is the probability that I pick a green one?

Number of Ways it can happen are 2 (there are 2 greens).

Number of Outcomes are 6 (there are 6 balls).

Probability = Ways / Outcomes

The probability that I pick a green one is 2 out of 6: 2/6 = 0.333333.

The probability is written P(green) = 0.333333.

P(A)W/OProbability
P(red)3/60.5000000
P(green)2/60.3333333
P(blue)1/60.1666666

P(A) = P(B)

P(A) = P(B)Event A and B have the same chance to occur
P(A) > P(B)Event A has a higher chance to occur
P(A) < P(B)Event A has a lower chance to occur

For the 6 balls:

P(red) > P(green)I am more likely to pick a red than a green
P(red) > P(blue)I am more likely to pick a red than a blue
P(green) > P(blue)I am more likely to pick a green than a blue
P(blue) < P(green)I am less likely to pick a blue than a green
P(blue) < P(red)I am less likely to pick a blue than a red
P(green) < P(red)I am less likely to pick a green than a red

Choosing a King

King

The probability of choosing a king in a deck of cards is 4 in 52.

Number of Ways it can happen are 4 (there are 4 kings).

Number of Outcomes are 52 (there are 52 cards).

Probability = Ways / Outcomes

The probability is 4 out of 52: 4/52 = 0.076923.

The probability is written P(king) = 0.076923.