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Coin Toss Probability Formula

  • Last Updated : 29 Dec, 2021

Probability is a branch of Mathematics. Probability tells how likely an event occurs. In a single word, it can be called a possibility i.e., the possibility of happening of an event. Its value always lies between 0 (zero) to 1 (one). 0 indicates an impossible event and 1 indicates a certain event. The formula for the probability of an event is mentioned below,

Probability of an event P(Event)= (Number of favorable outcomes)/ (Total number of possible outcomes)

Coin Toss Probability

Before going to the concept, first, let’s understand the possible outcomes when a coin is tossed. There are only 2 possible outcomes when a coin is tossed. Those are Head & Tail. So, as per the above probability formula, the coin toss probability formula is given as,

Coin Toss Probability Formula = (Number of favorable outcomes)/ (Total number of possible outcomes)

Here, when a single coin is tossed – Total number of possible outcomes = 2

So, simplify above formula for single coin toss as,

Coin Toss Probability Formula for single coin toss = (Number of favorable outcomes)/2

Sample Problems

Question 1: What is the probability of getting head when a single coin is tossed.

Solution: 

Let A be the event of getting head when a coin is tossed.

Number of favorable outcomes – {Head} = 1

As per the coin toss probability formula when a single coin is tossed, the probability of getting head P(A) = Number of favorable outcomes/2

P(A) = 1/2 = 0.5

So there is a 50% chance of getting head when a coin is tossed.

Question 2: What is the probability of getting at least 1 tail when two coins are tossed.

Solution: 

Let B be the event of getting at least 1 tail when two coins are tossed.

Number of favorable outcomes – {(Head, Tail), (Tail, Head), (Tail, Tail)} = 3

Total possible outcomes – {(Head, Tail), (Tail, Head), (Tail, Tail), (Head, Head)} = 4

As per the coin toss probability formula, Probability of getting atleast 1 tail when 2 coins are tossed P(B) = Number of favorable outcomes/Total number of possible outcomes

P(B) = 3/4 = 0.75

So there are 75% of chances of getting at least 1 tail when two coins are tossed.

Question 3: What is the probability of getting head or tail when two coins are tossed.

Solution: 

Let C be the event of getting head or tail when a coin is tossed.

Number of favorable outcomes – {Head, Tail} = 2

As per the coin toss probability formula when a single coin is tossed, the probability of getting head or tail P(C) = Number of favorable outcomes/2

P(C) = 2/2 = 1

So there is a 100% chance of getting head or tail when a single coin is tossed.

This is an example for sure (or) certain event.

Question 4: What is the probability of getting head and tail at the same time when a single coin is tossed.

Solution: 

Let D be the event of getting head and tail when a coin is tossed.

Here there are no favorable outcomes because when a coin is tossed only 1 possible outcome is obtained either a head or tail but both are not obtained.

Number of favorable outcomes – {} = 0

As per the coin toss probability formula when a single coin is tossed, Probability of getting head and tail P(D)= Number of favorable outcomes/2

P(D) = 0/2 = 0

So there are 0% chances of getting head and tail at the same time when a coin is tossed. 

This is an example of an impossible event.

Question 5: What is the probability of getting all three heads when 3 coins are tossed at same time.

Solution: 

Let E be the event of getting  all three heads when 3 coins are tossed.

When 3 coins are tossed the possible outcomes are ({HHH}, {HHT}, {HTH}, {THH}, {HTT}, {TTH}, {THT}, {TTT})

So total number of possible outcomes = 8

The total possible outcomes can also be found by multiplying the number of outcomes of each event together. Here 3 coins are tossed. For each coin toss, there will 2 outcomes. So by multiplying outcomes of each toss i.e., 2 × 2 × 2 = 8 total number of possible outcomes are obtained.

Number of favorable outcomes – {HHH} = 1

As per the coin toss probability formula, Probability of getting all three heads 

P(E) = Number of favorable outcomes/Total number of possible outcomes

P(E) = 1/8 = 0.125

So, there is 12.5% chances of getting all 3 heads when 3 coins are tossed.

Question 6: What is the probability of getting at least two heads when 3 coins are tossed at same time.

Solution: 

Let F be the event of getting atleast two heads when 3 coins are tossed.

When 3 coins are tossed the possible outcomes are ({HHH}, {HHT}, {HTH}, {THH}, {HTT}, {TTH}, {THT}, {TTT})

So, the total number of possible outcomes = 8

Number of favorable outcomes – ({HHT}, {HTH}, {THH}, {HHH}) = 4

As per the coin toss probability formula, the Probability of getting at least two heads

P(F)= Number of favorable outcomes/Total number of possible outcomes

P(F) = 4/8 = 1/2 = 0.5

So, there is 50% chance of getting atleast two heads when 3 coins are tossed.

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