Let's solve this step by step:
1. Identify the Individual Probabilities:
- Event [tex]\( A \)[/tex]: The first coin lands on heads.
The probability of a coin landing on heads is [tex]\( P(A) = 0.5 \)[/tex] or [tex]\( \frac{1}{2} \)[/tex].
- Event [tex]\( B \)[/tex]: The second coin lands on tails.
The probability of a coin landing on tails is [tex]\( P(B) = 0.5 \)[/tex] or [tex]\( \frac{1}{2} \)[/tex].
2. Use the Formula for Independent Events:
Since the events are independent, the probability of both events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring can be found using the formula:
[tex]\[
P(A \text{ and } B) = P(A) \cdot P(B)
\][/tex]
3. Substitute the Known Probabilities:
[tex]\[
P(A \text{ and } B) = 0.5 \cdot 0.5
\][/tex]
4. Calculate the Result:
[tex]\[
P(A \text{ and } B) = 0.25
\][/tex]
5. Express the Answer in Simplest Form:
The probability can be expressed in its simplest form as:
[tex]\[
P(A \text{ and } B) = \frac{1}{4}
\][/tex]
Therefore, the probability that both the first coin lands on heads and the second coin lands on tails is [tex]\(\frac{1}{4}\)[/tex] or [tex]\(0.25\)[/tex].
