Formula to Calculate Probability of a Coin Toss
The probability of any event that is supposed to or may happen is defined as the measurement of chances, or in simpler terms, the likelihood of this event occurring.
Now, the formula to calculate the probability of a coin toss can be defined as,
\(Probability=\frac{Number~of~favorable~outcomes}{Total~number~of~outcomes}\)
There are two possible outcomes when a coin is tossed. So, by applying the probability formula,
The probability of getting heads after the toss is: P(Heads) = P(H) = \(\frac{1}{2}\)
The probability of getting tails after the coin toss is: P(Tails) = P(T) = \(\frac{1}{2}\)
Solved Examples
Example 1: If a coin is tossed thrice, what is the probability of getting at least two tails?
Solution:
When a coin is tossed thrice, the possible outcomes are {HHH, TTT, HHT, HTH, THH, HTT, TTH, THT}
Total number of outcomes is 8.
The number of desired outcomes of getting two tails is {HTT, TTH, THT, TTT}
The count for the number of favorable outcomes is 4.
Thus, the probability of getting at least two tails = \(\frac{Number~of~favorable~outcomes}{Total~number~of~outcomes}\)
= \(\frac{4}{8}\)
= \(\frac{1}{2}\)
The probability of getting at least two tails is \(\frac{1}{2}\).
Example 2: What is the probability of getting at least one heads when two coins are tossed simultaneously?
Solution:
When two coins are tossed, the possible outcomes will be {HH, TT, HT, TH}.
Hence, the total number of possible outcomes = 4
The number of desirable outcomes for getting at least one heads will be {HT, TH} outcomes.
Thus, the number of favorable outcomes = 2
Hence, the probability of getting at least one heads = \(\frac{Number~of~favorable~outcomes}{Total~number~of~outcomes}\)
= \(\frac{2}{4}\)
= \(\frac{1}{2}\)
The probability of getting at least one heads is \(\frac{1}{2}\).
Example 3: What is the probability of getting the same face when a coin is tossed twice?
Solution:
When two coins are tossed, the possible outcomes will be {HH, TT, HT, TH}.
Thus, the total number of outcomes = 4
The desirable outcomes of the same face will be {HH, TT}
Number of desirable outcomes = 2
Thus the probability of getting the same face = \(\frac{Number~of~favorable~outcomes}{Total~number~of~outcomes}\)
= \(\frac{2}{4}\)
= \(\frac{1}{2}\)
Thus, the probability of getting the same face is \(\frac{1}{2}\).
In mathematics, probability denotes the possibility of the outcomes of any random experiment.
Events in probability can be defined as a specific set of outcomes for a random experiment.
Simple events can be defined as any event that comes with a single point of the sample space. For example, if S = {23, 45, 68, 72} and E = {72}, then E is a simple event.
Exhaustive events are those events, where at least one of them definitely occurs during an experiment.