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.
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To find the probability that the 4th toss is a tail, given that the first 3 tosses were all heads, we need to use conditional probability.
First, let's determine the sample space. Since a coin is tossed 4 times, each toss can result in either a head (H) or a tail (T). Thus, there are 2^4 = 16 possible outcomes in the sample space.
Now, let's focus on the condition that the first 3 tosses are heads (HHH). Since we are given that the first 3 tosses were heads, we can reduce the sample space to only include these outcomes.
Out of the 16 possible outcomes, only 1 satisfies the condition (HHHH). Hence, there is only 1 outcome in the reduced sample space that satisfies the condition.
Now, let's determine the number of outcomes in the reduced sample space where the 4th toss is a tail. Since there is only 1 outcome in the reduced sample space (HHHH), and the 4th toss is not a tail, there are 0 outcomes where the 4th toss is a tail.
Therefore, the probability that the 4th toss is a tail, given that the first 3 tosses were all heads, is 0.