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A fair coin is tossed n times. Show that the probability of getting an even number of heads is.

A fair coin is tossed n times. Show that the probability of getting an even number of heads is.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 17: Coin Toss Probability** A fair coin is tossed \( n \) times. Show that the probability of getting an even number of heads is \( \frac{1}{2} \). This problem involves understanding the probability of a specific outcome when a fair coin is tossed multiple times. The solution will explore the properties of binomial distributions and symmetry in probabilities.
Transcribed Image Text:**Problem 17: Coin Toss Probability** A fair coin is tossed \( n \) times. Show that the probability of getting an even number of heads is \( \frac{1}{2} \). This problem involves understanding the probability of a specific outcome when a fair coin is tossed multiple times. The solution will explore the properties of binomial distributions and symmetry in probabilities.
Expert Solution
Step 1

Given:

A fair coin is tossed n times.

To Prove:

The probability of getting an even number of heads is 12.

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