Probability of Obtaining Heads and Tails Alternately

To find the probability of obtaining Heads and Tails alternately, we need to consider the possible outcomes of flipping a coin six times. There are 2 possible outcomes for each flip, Heads or Tails. Therefore, there are 2^6 = 64 possible outcomes for flipping a coin six times.

Outcomes of Flipping a Coin Six Times

To find the outcomes of flipping a coin six times, we can use a tree diagram. The first level of the tree diagram represents the first flip, and the second level represents the second flip, and so on. The branches of the tree represent the possible outcomes of each flip.

For example, the first level of the tree diagram would have two branches, one for Heads and one for Tails. The second level would have two branches for each branch of the first level, resulting in four branches in total. The third level would have eight branches, and so on.

Counting the Outcomes

To count the outcomes where Heads and Tails appear alternately, we need to look for patterns in the tree diagram. We can see that there are three possible patterns:

- HTHTHT
- THTHTH
- HTHTH

Each pattern has two possible outcomes, one where the first flip is Heads and one where the first flip is Tails. Therefore, there are a total of 6 possible outcomes where Heads and Tails appear alternately.

Calculating the Probability

To calculate the probability of obtaining Heads and Tails alternately, we need to divide the number of possible outcomes where Heads and Tails appear alternately by the total number of possible outcomes:

P(HT alternately) = 6/64 = 0.09375

Therefore, the probability of obtaining Heads and Tails alternately when flipping a coin six times is 0.09375 or approximately 9.4%.

Total outcomes, n(s)= 2^6=64