To determine the probability that Claire's coin will show tails at least once when she flips it 4 times, we can follow these steps:
1. Understand the Problem:
- We are looking for the probability that there is at least one tails in 4 coin flips.
2. Use the Complement Rule:
- The complement rule in probability states that the probability of at least one tails is equal to 1 minus the probability of getting no tails at all.
- In simpler terms: [tex]\( P(\text{at least one tails}) = 1 - P(\text{no tails}) \)[/tex].
3. Identify the Given Probabilities:
- According to the provided table, the probability of flipping 0 tails (which means getting heads in all 4 flips) is 0.06.
4. Apply the Complement Rule:
- Using the complement rule, the probability of getting at least one tails is:
[tex]\[
P(\text{at least one tails}) = 1 - P(\text{no tails})
\][/tex]
- Substituting the given probability:
[tex]\[
P(\text{at least one tails}) = 1 - 0.06
\][/tex]
5. Calculate the Probability:
- Perform the subtraction:
[tex]\[
P(\text{at least one tails}) = 1 - 0.06 = 0.94
\][/tex]
Therefore, the probability that the coin will show tails at least once when Claire flips it 4 times is 0.94.
