Data Science Interview Prep: Q66
Guess the First Toss — With Just k Heads in n Fair Coin Tosses. (Category: Probability)
A fair coin is tossed n times, resulting in exactly k heads. Given this, what is the probability that the first toss was a head?
Solution:
We’re told that exactly k heads appeared in n coin tosses. Our goal is to find the probability that the first toss was one of those heads.
Total number of ways of obtaining k heads in n coin tosses:
If the first coin toss is a tail, then the probability of obtaining k heads in the remaining (n-1) coin tosses:
The probability of having tails in the first coin toss is:
We must recognize that the probability of getting heads on the first toss, plus the probability of getting tails on the first toss, equals 1. Using the result from equation (3), we obtain the following expression:
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Reference:
Determining the First Toss Outcome: https://brainly.com/question/32901848