A coin is flipped independently several times. Let the event A; represent a head (H) on the ith toss; thus A represents a tail (T). Assume that A; and A are equally likely. Find the probabilities of observing sequence like: 1. HHTH 2. TTHT 3. getting at least one head

A coin is flipped independently several times. Let the event A; represent a head (H) on the ith toss; thus A represents a tail (T). Assume that A; and A are equally likely. Find the probabilities of observing sequence like: 1. HHTH 2. TTHT 3. getting at least one head

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A coin is flipped independently several times. Let the event A; represent a head (H) on the ith toss; thus A represents a tail
(T). Assume that A; and A are equally likely. Find the probabilities of observing sequence like:
1. HHTH
2. TTHT
3. getting at least one head

Expert Solution

Step 1: Probabilities obtained.

Coin is flipped 4 times, the sample space contains $2 to the power of 4 space equals 16$ sample points. Since getting of H and T is equally likely

P(H) = $1 half$ = P(T) or, P( $A subscript i right parenthesis space equals space 1 half space equals space P left parenthesis A subscript i to the power of c right parenthesis$ , therefore,

1. P(HHTH) = $1 over 16$

2. P(TTHT) = $1 over 16$

3. Sample Space S contains 16 sample points in which only sample point TTTT does not have H

Therefore P(Getting atleast one Head) is = $15 over 16$

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