Final answer:
The probability of getting anything except 3 heads when you toss three fair coins at once is 1, or 100%.
Step-by-step explanation:
The probability of getting anything except 3 heads when you toss three fair coins at once can be calculated by finding the probability of getting 0, 1, 2, or 3 tails. Since there are 2 possible outcomes (heads or tails) for each coin toss, and three coins are being tossed, there are a total of 2^3 = 8 possible outcomes.
Now, let's calculate the probability of getting 0 tails:
- The probability of getting a head on the first coin toss is 1/2.
- The probability of getting a head on the second coin toss is also 1/2.
- The probability of getting a head on the third coin toss is again 1/2.
The probability of getting 0 tails is (1/2) * (1/2) * (1/2) = 1/8.
Similarly, if we calculate the probabilities of getting 1, 2, or 3 tails using the same approach, we get:
The probability of getting 1 tail is 3/8.
The probability of getting 2 tails is 3/8.
The probability of getting 3 tails is 1/8.
To find the probability of getting anything except 3 heads, we add up the probabilities of getting 0, 1, 2, or 3 tails:
(1/8) + (3/8) + (3/8) + (1/8) = 8/8 = 1.
Therefore, the probability of getting anything except 3 heads when you toss three fair coins at once is 1, or 100%.