1101 LearnersLast updated on June 4th, 2025
Tossing a Coin
A coin has two sides - heads and tails. Tossing a coin involves throwing the coin in the air to determine an outcome, typically heads or tails. It is based on chance, and we need to guess the right outcome. In this topic, we are going to talk about tossing a coin and why we use it.
What Are the Possible Events that Can Occur When A Coin Is Tossed?
When flipping a coin, there are two possible outcomes: Heads or tails. If a coin is tossed several times there can be several other possible outcomes, the sample space of these outcomes for a single toss can be {Head, tail) or {H, T} for multiple tosses it can be {HH], {HT}, {TT}, {TH}. If you toss the coin more than once, then the number of possible outcomes increases. For example, If you toss a coin twice, then the possible outcomes are:
HH (Heads, Heads)
HT (Heads, Tails)
TH (Tails, Heads)
TT (Tails, Tails)
Each extra toss doubles the number of possible outcomes. If the coin toss is fair, which means that no outcome is preferred, then every outcome is equally likely. In a fair coin toss, the number of heads should be almost half of the total tosses, the same will be applied to tails.
Why do we use flip a coin?
We use a coin toss as an impartial decision-making tool. Some features of flipping a coin are:
- The outcomes of a coin toss is random and each result is based on chance.
- It is a widely used method of making decisions, which makes it a very common tool.
- Flipping a coin provides a quick resolution for any kind of decision-making.
How to use probability in Tossing a coin
When we toss a coin we do not know which outcome we will obtain, whether heads or tails. But one thing we do know is that it will land on heads or tails (we can rule out the coin landing on its edge). Since we do not know what the outcome of tossing a coin will be, we use a general formula to determine the probability:
Probability = Number of favourable outcomes / Total number of outcomes
When a coin is tossed, there are only two outcomes that can happen
Therefore, using the probability formula, we can determine the chance of getting heads or tails.
Solved Examples on Tossing a Coin
Problem 1
What is the probability of getting heads when a fair coin is tossed once?
1/2
Explanation
Since a coin has two sides, the total number of possible outcomes is 2.
The number of ways to get heads is 1, so the probability is:
Number of favourable outcomes/Total number of outcomes = 1/2
Problem 2
What is the probability of getting at least one head in two tosses?
3/4
Explanation
The favorable outcomes are: HH, HT, TH (3 out of 4 total outcomes) = 3/4
Problem 3
What is the probability of getting at least one tail in five tosses?
31/32
Explanation
The only case where there is a chance of getting no tails is HHHHH. So the chance of getting tails at least once is: Total number of outcomes is 25 = 32
1 - 1/32 = 31/32
Problem 4
What is the probability of getting exactly two heads in four tosses?
6/16 = 3/8
Explanation
The possible sequences with 2 heads: HHTT, HTHT, HTTH, THHT, THTH, TTHH (6 WAYS).
Total outcomes: 24 = 16.
6/16 = 3/8
Problem 5
What is the probability of getting at least one head in 10 tosses?
1 - 1/1024 = 1023/1024
Explanation
The only unfavorable outcome is all tails (TTTTTTTTTT), which occurs once in 210 = 1024 cases.
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