Answer:
1/4
Explanation:
It is really weird that this answer is not on there but here is my explanation.
We can consider this question in two different ways.
First, we could list the possible outcomes.
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
In total 8 possibilities, 2 of which are either all heads or all tails. So the probability is 2/8 which is 1/4.
Alternatively, we could look at each of the three independent events in turn.
We toss the first coin. We don’t mind whether it lands head or tail, but we need to note the result. The probability of getting any result is 1.
We toss the second coin and there is a probability of 1/2 that the result matches the first toss.
We now toss the third coin and again there is a probability of 1/2 that the result matches the first toss.
So the probability of getting all heads or all tails is the probability of getting any result from the first toss (1) multiplied by the probability of a matching result for the second toss (1/2) multiplied by the probability of a matching result for the third toss (1/2).
So that’s 1 * (1/2) * (1/2), which is 1/4.