A fair coin is tossed 4 times. Complete parts​ (A) and​ (B) below.
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Part 1
If a fair coin is tossed one​ time, then the probability of tossing a tail is

. 5.
​(Type an integer or a simplified​ fraction.)
Part 2
left parenthesis Upper A right parenthesis What is the probability of tossing a tail on the 4 th ​toss, given that the preceding 3 tosses were heads​?

**Part 1: Probability of Tossing a Tail in One Toss**

If a fair coin is tossed one time, the probability of tossing a tail is:

\[
\frac{1}{2} \text{ or } 0.5
\]

**Part 2: Probability of Tossing a Tail on the 4th Toss Given That the Preceding 3 Tosses Were Heads**

For each coin toss, the outcome is independent of the previous tosses. This means that the result of the 4th toss is unaffected by the first three tosses. 

Thus, the probability of getting a tail on the 4th toss is still:

\[
\frac{1}{2} \text{ or } 0.5
\]

This is because each toss of a fair coin has an equal chance of landing on either heads or tails, regardless of the results of any prior tosses.

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Would you like more details, or do you have any questions?

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Here are 5 related questions to explore further:

1. What is the probability of getting exactly 2 tails in 4 tosses of a fair coin?
2. What is the probability of getting at least one tail in 4 tosses?
3. How does the probability change if we increase the number of tosses to 5?
4. How many possible outcomes are there in 4 coin tosses?
5. If a biased coin has a 0.6 probability of heads, what’s the probability of getting a tail on the 4th toss?

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**Tip:** For independent events, previous outcomes do not affect the probability of future outcomes. This concept is often crucial when dealing with coin tosses, dice rolls, and similar experiments.

A fair coin is tossed 4 times. Complete parts (A) and (B) below. Part 1: If a fair coin is tossed one time, then the probability of tossing a tail is .5. (Type an integer or a simplified fraction.) Part 2: What is the probability of tossing a tail on the 4th toss, given that the preceding 3 tosses were heads?

Explore the probability of getting a tail in a fair coin toss. Part A covers calculating the probability of a single tail, while Part B examines the probability on the 4th toss, given that the first three were heads. This problem introduces probability and independence concepts, suitable for students in Grades 6-8.

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