Flipping a coin

Question

What is the probability that no consecutive heads occur on three tosses of a coin?

Answer 1

Method 1.

List all elements in sample space:

1.  HHH

2.  HTH x

3.  HHT

4.  HTT x

5.  TTT x

6.  THT x

7.  TTH x

8.  THH

So, P(no consecutive heads occur on three tosses of a coin) = 5/8

 

 

Method 2. Focus on the middle first.

Case 1: _T_: 2^2 ways to insert H or T on the two empty positions

Case 2: _H_: 1 way only THT.

So, the answer is (2^2 + 1)/2^3 = 5/8

Answer 2

"What is the probability that no consecutive heads occur on three tosses of a coin?"  This can be interpreted to include any occurrences of HH as well as HHH on the 3 tosses.

 

Using Vivian's set of all possibilities, "no consecutive heads" appear on outcomes 2,4,5,6, and 7.  That is 5 of the 8 equally likely outcomes (since P(H)=P(T)=.5).  Therefore the probability that no consecutive heads occur = 5/8 = 0.625.

Answer 3

Hi Chris;

There is a long approach and short approach to this.

 

Let's begin with the long.  These are all the possibilities...

 

1.  HHH

2.  HTH

3.  HHT

4.  HTT

5.  TTT

6.  THT

7.  TTH

8.  THH

 

The probability is 1/8.

 

This is the short approach...

1/2³=probability

 

The number 2 is the total possibilities-per-toss; head or tail.

The number 3 is the total number of tosses.