There is no relationship between sequences and probability.
Chat with our AI personalities
There are factors such as genetic tendencies, age etc which favour male or female offspring so that the probability of a male offspring is not uniformally 1/2. Next, the question does not specify how many offspring in all, so the possible sequences could be [any sequence whether or not containing MMM] followed by [MMM] followed by [any sequence whether or not containing MMM]. As the sequence grows longer, the probability that somewhere in the sequence there are 3 male offspring in a row increases. For 3 offspring, the probability is 1/8 = 0.125 for 8 offspring, the probability is 107/256 = 0.418 The probabilities would need to be weighted together using the proportion of families that have 3 children, 4 children, and so on.
Assuming the coin is fair, the probability of that sequence is 1/16. The probability of three H and one T, in any order, is 1/4.
The probability of getting a head first time is one out of two, or a half. The probability of getting a head the next time is still one out of two, so the combined probability is one quarter. Similarly, one eighth is the probability of getting three in a row; but the pattern does not end there, the probability of getting a tails the next time is STILL one in two, so that is a one in sixteen chance of that run, the probability of the entire sequence is therefore one in thirty-two.
If you're talking with probability then it's the middle number of a sequence. Eg ( 2 3 4 5 6 7)- The mode is 4.
The key word that I use is causality. However, you cannot use probability to determine causality. Even if two events are highly correlated, probability theory cannot tell whether event A is caused by event B, or event B is caused by event A, or that both are caused by some third event that is not even part of the study.