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Coin Toss Probability Formula

Last updated date: 17th May 2024
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What is the Coin Toss Probability Formula?

Let's look at a few things about flipping a coin before studying the coin toss probability formula. There are two potential consequences when flipping a coin: heads or tails. We don't know which way the coin will land on a given toss, but we do know it will either be Head or Tail. Tossing a coin, on the other hand, is a random experiment since you know the set of outcomes but not the exact outcome for each random experiment execution. 

The probability formula for a coin flip can be used to calculate the probability of some experiment. This page discusses the concept of coin toss probability along with the solved examples.

Results of Coin Toss Probability 

Each result has a predetermined likelihood, which remains constant from trial to trial. Heads and tails share the same chance of 1/2 when it comes to coins. In addition, there are cases where the coin is skewed, resulting in varying odds for heads and tails. In this part, we'll look at probability distributions with just two potential outcomes and fixed probabilities that add up to one. Binomial distributions are the name for certain types of distributions.

Here are some examples of problems involving coin toss chances.

If a coin is flipped, there are two potential outcomes: a ‘head' (H) or a ‘tail' (T), and it is difficult to determine whether the toss will end in a ‘head' or a ‘tail.' 

Assuming the coin is equal, then the coin probability is 50% or 1/2 

This is because you know the result would be either head or tail, and both are equally probable.

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The Probability for Equally Likely Outcomes is:

Total number of favorable outcomes  and Total number of possible outcomes


Total number of possible outcomes = 2

  1. Coin toss probability formula for heads

If the favorable outcome is head (H).

A number of favorable outcomes = 1.

Therefore, P (getting heads) = \[ \frac{number \, of \, favorable \, outcomes}{total \, number \, of \, possible \, outcomes} = \frac{1}{2} \]

  1. Coin toss probability formula for tails.

If the favorable outcome is tail (T).

A number of favorable outcomes = 1.

Therefore, P (getting heads) = \[ \frac{number \, of \, favorable \, outcomes}{total \, number \, of \, possible \, outcomes} = \frac{1}{2} \]

Coin Probability Problems

  1.  A Coin is Tossed Thrice at Random. What is the Probability of Getting

  1. At Least One Head

  2. The Same Face?


The possible outcomes of a given event are {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

So, the total number of outcomes = 8.

  1. Number of favorable outcomes for event E

  = Number of outcomes appears at least one head

  = 4 (as HHH, HHT, HTH, HTT, THH, THT, TTH are having at least one head).

  = 7/8

So, by definition, P(F) = 7/8

  1. Number of favorable outcomes for event E

   = Number of outcomes having the same face

   = 2 (as HHH, TTT has the same face).

   = 2/8

   = 1/4

So, by definition, P(E) = ¼

  1. What is the Probability of Getting a Head When Tossing a Coin?


When a single coin is tossed, the possible outcomes can be {H, T}.

Thus, the total number of possible outcomes = 2

Getting ahead includes {H} outcomes.

So the number of favorable outcomes = 1


the probability of getting head is,

P(H) = Number of Favorable Outcomes/Total Number of Possible Outcomes

 = 1/2 

So, by definition P(H) = ½

3. Two Coins are Tossed Randomly 150 Times and it is Found That Two Tails Appeared 60 Times, One Tail Appeared 74 Times and No Tail Appeared 16 Times.

If two coins are tossed at random, then what is the probability of,

  1. Getting 2 Tails

  2. Getting 1 Tail

  3. Getting 0 Tail


Total number of trials = 150

Number of times 2 tails appear = 60 

Number of times 1 tail appears = 74

Number of times 0 tail appears = 16

Let T1, T2, and T3 be the events of getting 2 tails, 1 tail and 0 tail respectively.

  1. P(getting 2 tails)

The number of times two tails appear is 60.

= P(T1) =   Number of Times two Tails Appears/Total Number of Possible Outcomes

= 60/150

= 0.40

The probability of getting 2 tails is 0.40

  1. P(getting 1 tail)

The number of times one tail appears is 74

= P(T2) =  Number of Times one Tail AppearsTotal Number of Possible Outcomes

= 74/150

= 0.4933

The probability of getting one tail is 0.4933

  1. P(getting 0 tail)

The number of times zero tail appear is 16

= P(T3) = Number of Times Zero Tail AppearsTotal Number of Possible Outcomes

= 16/150

= 0.1067

The probability of getting zero tail is 0.1067


Remember while tossing 2 coins simultaneously, the only possible outcomes are T1, T2, T3, 

= P (T1) + P (T2) + P (T3)

= 0.40 + 0.4933 + 0.1067

= 1

FAQs on Coin Toss Probability Formula

1. What is the Sample Space When Four Coins are Tossed?

Four coins are tossed simultaneously, then the sample space is,

Tossed coins = 4

Hence, The number of faces  = 24= 16


2. Where Did the Coin Toss Originate From?

The view of a random result as an act of divine will is the historical basis of coin-flipping.

The Romans named coin flipping Navia Aut Caput ("ship or head") since certain coins had a ship on one hand and the emperor's head on the other. This was known as cross and pile in England.

3. Who Won the Super Bowl 2020 Coin Toss?

In the 2020 year, the 49ers won the Super Bowl LIV coin toss after picking tails.

4. What is the probability of getting heads if you flip a coin 3 times?

On flipping a coin 3 times the probability of getting 3 heads, we get total eight outcomes as {HHH, THH, HTH, HHT, TTH, THT, HTT, TTT}

Total outcomes are - 8 and among these three heads has one outcome only. 

Now, use the coin toss probability formula and apply the values below:

P (getting three heads) =number of favorable outcomestotal number of possible outcomes = 18

Therefore, P (getting three heads) = 0.125.