To determine the probability that Claire will get tails at least once when flipping a coin 4 times, let's analyze the given data step by step.
1. Understanding the Probabilities:
- The table provides the probabilities of getting a certain number of tails (0, 1, 2, 3, or 4) in 4 coin flips.
- Specifically, it gives:
- The probability of 0 tails (all heads) is 0.06.
- The probability of 1 tail is 0.25.
- The probability of 3 tails is 0.25.
- The probability of 4 tails is 0.06.
2. The Missing Probability:
- To find the probability of 2 tails, we must note that the sum of all probabilities for all possible outcomes is 1.
- Probability(0 tails) + Probability(1 tail) + Probability(2 tails) + Probability(3 tails) + Probability(4 tails) should equal 1.
- Given that:
[tex]\[
0.06 + 0.25 + P(2) + 0.25 + 0.06 = 1
\][/tex]
- We can solve for [tex]\( P(2) \)[/tex]:
[tex]\[
0.62 + P(2) = 1
\][/tex]
[tex]\[
P(2) = 1 - 0.62 = 0.38
\][/tex]
- Therefore, the probability of getting exactly 2 tails in 4 flips is 0.38.
3. Calculating Probability of At Least One Tail:
- The event “at least one tail” is the complement of the event “no tails” (0 tails).
- The probability of no tails (all heads), as given in the table, is 0.06.
- Therefore, the probability of getting at least one tail is:
[tex]\[
1 - \text{Probability(0 tails)} = 1 - 0.06 = 0.94
\][/tex]
Thus, the probability that Claire will get tails at least once in 4 coin flips is [tex]\( \boxed{0.94} \)[/tex].
