Tossing a coin probability formula

The coin toss probability formula helps us find the chance of getting a head or a tail. When you flip a fair coin, there are two possibilities . Each possibility is equally likely. This makes the topic easy to understand for the students. It is often used in mathematics and basic probability problems. Children feel confident comparing possible outcomes and solving basic questions when they know this formula. A coin toss is a good example. Easy, familiar, and fair. It also gives a good basis for later classes in learning more about probability.

What Is Tossing a Coin in Probability?

A coin toss is used in probability because it is a fair and random experiment. A fair coin has exactly two sides heads (H) and tails (T) and neither side is more likely to appear than the other.

Each outcome has an equal chance of occurring.

Random Outcomes in a Coin Toss

Each coin toss is independent. The result of one toss does NOT affect the next toss. This makes it a random experiment you cannot predict the exact result in advance.

Possible Outcomes of Tossing a Coin

Sample Space of One Coin Toss

The sample space is the set of all possible outcomes.

One coin toss:

Sample Space (S) = {H, T}

Total outcomes = 2

H = Heads

T = Tails

Outcomes of Two Coin Tosses

Two coins tossed together:

Sample Space = {HH, HT, TH, TT}

Total outcomes = 4

HH = Both heads

HT = First head, second tail

TH = First tail, second head

TT = Both tails

Outcomes of Three Coin Tosses

Three coins tossed together:

Sample Space = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Total outcomes = 8

Total outcomes formula: 2ⁿ

Where n = number of coins

1 coin → 2¹ = 2 outcomes

2 coins → 2² = 4 outcomes

3 coins → 2³ = 8 outcomes

Probability of Tossing a Coin

Formula for Probability

                 Number of favorable outcomes
P(Event) =   _____________________________
                  Total number of possible outcomes

P(E) = n(E) / n(S)

Probability of Getting a Head

One coin toss:

Favorable outcome = {H} → 1 outcome

Total outcomes = 2

P(Head) = 1/2 = 0.5 = 50%

Probability of Getting a Tail

One coin toss:

Favorable outcome = {T} → 1 outcome

Total outcomes = 2

P(Tail) = 1/2 = 0.5 = 50%

Note: P(H) + P(T) = 1/2 + 1/2 = 1 

(All probabilities must sum to 1)

Tossing Two Coins in Probability

Sample Space of Two Coin Tosses

TWO COIN TOSS TABLE:

Coin 1	Coin 2	Outcome
H	H	HH
H	T	HT
T	H	TH
T	T	TT

Total outcomes = 4

Probability of Different Outcomes

P(both heads) = P(HH) = 1/4

P(one head, one tail) = P(HT or TH) = 2/4 = 1/2

P(both tails) = P(TT) = 1/4

P(at least one head) = P(HH,HT,TH) = 3/4

P(exactly one head) = P(HT,TH) = 2/4 = 1/2

Probability Table

Tossing Three Coins in Probability

Sample Space

Sample Space = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Total outcomes = 8

Probability of Getting Exactly One Head

Outcomes with exactly one head: {HTT, THT, TTH}

Favorable outcomes = 3

P(exactly one head) = 3/8

Probability of Getting Two Heads

Outcomes with exactly two heads: {HHT, HTH, THH}

Favorable outcomes = 3

P(exactly two heads) = 3/8

Probability of Getting Three Heads

Outcomes with three heads: {HHH}

Favorable outcomes = 1

P(three heads) = 1/8

Three Coin Probability Summary:

Probability Tree Diagram for Coin Tossing

Tree Diagram for One Toss

Tree Diagram for Two Tosses

 

Total = 4 branches, each with P = 1/4

Sum = 4 × 1/4 = 1

Formula for Tossing a Coin in Probability

Probability Formula

P(Event) = n(E) / n(S)

 Where:

n(E) = number of favorable outcomes

n(S) = total number of outcomes

Number of Outcomes Formula

Total outcomes for n coins = 2ⁿ

Examples:

1 coin: 2¹ = 2

2 coins: 2² = 4

3 coins: 2³ = 8

4 coins: 2⁴ = 16

10 coins: 2¹⁰ = 1024

Solved Examples on Tossing a Coin

Example 1: One Coin Toss

Question: A fair coin is tossed once. Find the probability of getting a tail.

Solution:

Sample Space = {H, T}

n(S) = 2

Favorable outcome = {T}

n(E) = 1

P(Tail) = 1/2

Answer: P(Tail) = 1/2

Example 2: Two Coin Tosses

Question: Two coins are tossed simultaneously. Find the probability of getting at least one head.

Solution:

Sample Space = {HH, HT, TH, TT}

n(S) = 4

Favorable outcomes = {HH, HT, TH} → 3 outcomes

P(at least one head) = 3/4

Answer: P(at least one head) = 3/4

Example 3: Three Coin Tosses

Question: Three coins are tossed at once. Find the probability of getting exactly two tails.

Solution:

Sample Space = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

Outcomes with exactly two tails:

{HTT, THT, TTH} → 3 outcomes

P(exactly two tails) = 3/8

Answer: P(exactly two tails) = 3/8

Practice Questions on Tossing a Coin

Basic Questions

Q1: What is the sample space when one coin is tossed?

Answer: {H, T}

Q2: What is the total number of outcomes when two coins are tossed?

Answer: 4 (= 2²)

Q3: Find P(getting all heads) when 3 coins are tossed.

Answer: 1/8

Q4: What is P(H) + P(T) for a fair coin?

Answer: 1/2 + 1/2 = 1

Multiple Choice Questions

Q5: A coin is tossed twice. What is P(both tails)?

a) 1/2    b) 1/4    c) 1/3    d) 3/4

Answer: b) 1/4

Q6: Three coins are tossed. P(at least one tail) = ?

a) 1/8    b) 3/8    c) 7/8    d) 5/8

Answer: c) 7/8

(Complement of all heads: 1 − 1/8 = 7/8)

Q7: Total outcomes when 4 coins are tossed?

a) 8    b) 12    c) 16    d) 4

Answer: c) 16 (= 2⁴)

Word Problems on Tossing a Coin

Q8: Ravi and Priya toss a coin to decide who bats first. What is the probability that Ravi wins the toss?

Solution:

P(Ravi wins) = P(getting the chosen side) = 1/2

Answer: 1/2

Q9: A teacher tosses two coins in class. Find P(getting exactly one tail).

Sample Space = {HH, HT, TH, TT}

Exactly one tail = {HT, TH} → 2 outcomes

P = 2/4 = 1/2

Answer: 1/2