Question

A fair coin is tossed 2 times in succession. The set of equally likely outcomes is StartSet HH comma HT comma TH comma TT EndSet. Find the probability of getting a head on the second toss.
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Part 1
The probability of getting a head on the second toss is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)

Answer 1

To find the probability of getting a head on the second toss when a fair coin is tossed twice, we can analyze the sample space.

The possible outcomes from tossing a coin twice are:
- HH (Head on first toss, Head on second toss)
- HT (Head on first toss, Tail on second toss)
- TH (Tail on first toss, Head on second toss)
- TT (Tail on first toss, Tail on second toss)

The total number of outcomes is 4.

Now, let’s identify the outcomes that result in getting a head on the second toss:
- HH (Head on first, Head on second)
- TH (Tail on first, Head on second)

Thus, there are 2 favorable outcomes (HH and TH) where the second toss is a head.

Now, we can calculate the probability of getting a head on the second toss:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{4} = \frac{1}{2}
\]

Therefore, the probability of getting a head on the second toss is:

\[
\frac{1}{2}
\]