A coin has probability p (0

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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The image contains the following mathematical problem related to coin toss probabilities:

---

A coin has a probability \( p \) \((0 < p < 1)\) of coming up heads and \( 1 - p \) of coming up tails.

(a) Calculate the probability that if the coin is tossed \( n \) times, the number of heads obtained is even.

(b) Evaluate the limit of the probability in (a) as \( n \to \infty \).

--- 

This problem involves understanding the concept of probability in the context of repeated independent events and examines how the distribution of outcomes changes as the number of trials increases indefinitely.
Transcribed Image Text:The image contains the following mathematical problem related to coin toss probabilities: --- A coin has a probability \( p \) \((0 < p < 1)\) of coming up heads and \( 1 - p \) of coming up tails. (a) Calculate the probability that if the coin is tossed \( n \) times, the number of heads obtained is even. (b) Evaluate the limit of the probability in (a) as \( n \to \infty \). --- This problem involves understanding the concept of probability in the context of repeated independent events and examines how the distribution of outcomes changes as the number of trials increases indefinitely.
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