To determine the probability of getting at least one head when a coin is tossed three times, it can be easier to first calculate the probability of the opposite event—that is, getting no heads at all.
When a coin is tossed, there are two possible outcomes: heads (H) or tails (T). The probability of getting tails in a single toss is 1/2 or 50%.
Now, if we toss the coin three times, the probability of getting tails each time is:
P(Tails in 3 tosses) = P(T) 23 = (1/2) 23 = 1/8.
This means that the probability of getting no heads in three tosses (i.e., getting tails all three times) is 1/8.
Since the total probability of all possible outcomes must equal 1, we can find the probability of getting at least one head by subtracting the above result from 1:
P(At least one head) = 1 – P(No heads) = 1 – 1/8 = 7/8.
Therefore, the probability of getting at least one head when a coin is tossed three times is 7/8, or approximately 87.5%.