Probability In an experiment, three people toss a fair coin one at a time until one of them tosses a head. Determine, for each person, the probability that he or she tosses the first head.
Verify that the sum of the three probabilities is 1.
To calculate: The probability of each person getting the first head. Also, verify if the sum of probabilities equals 1.
Three people tossing a coin at a time until one of them tosses a head.
Let , where p is the probability of an event.
The sum of G.P. with first term as a and common ratio as r is,
Since, the coin could theoretically give a very large number of tails first, so, each person’s probability is made up of an infinite series.
So, the probability when the first person gets the first head is given by,
Since, this is an infinite geometric series with
Its sum is,
Now, the probability when the second person gets the first head is given by,
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