A coin is tossed 4 times. Find the probability that the 4th toss is a tail, given that the first 3 tosses were all heads.
To find the probability that the 4th toss is a tail, given that the first 3 tosses were all heads, we can use conditional probability.
Let's start by calculating the probability of getting all heads in the first 3 tosses. Since each toss is independent and has a probability of 1/2 of being heads, the probability of getting heads in all 3 tosses is (1/2) * (1/2) * (1/2) = 1/8.
Now, we need to find the probability that the 4th toss is a tail, given that the first 3 tosses were all heads. Since the first 3 tosses were already heads, we are only interested in what happens on the 4th toss. Since the coin has two equally likely outcomes (heads or tails) and the first 3 tosses were all heads, we can assume that the coin is fair and that the probability of getting a tail on the 4th toss is also 1/2.
Therefore, the probability that the 4th toss is a tail, given that the first 3 tosses were all heads, is 1/2.
To summarize, the probability that the 4th toss is a tail, given that the first 3 tosses were all heads, is 1/2.