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.
1 out of 555555
If the sequence matters (you want H-H-T in that order), then . . .Probability of the first head = 0.5Probability of the second head = 0.5Probability of the tail on the 3rd toss = 0.5Probability of the correct 3-toss sequence = (0.5 x 0.5 x 0.5) = 1/8 = 0.125 = 12.5%=====================================================If the sequence doesn't matter, then the probability is higher.All the possible results of 3 tosses are:TTTTTHTHTTHHHTTHTHHHTHHHIf the sequence doesn't matter, there are 3 different ways to get 2 heads and 1 tail.The probability is3/8 = 0.375 = 37.5%
No, but it can represent the probability of such an outcome.
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.
Probability of the first head = 0.5Probability of the second head = 0.5Probability of the tail on the 3rd toss = 0.5Probability of the correct 3-toss sequence = (0.5 x 0.5 x 0.5) = 1/8 = 0.125 = 12.5%
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.
If you toss the die often enough then the probability of getting the sequence 2-2-1 is 1: a certainty. The probability of getting the result in the first three tosses is 1/216.
Say there are n possible input sequences that is A1 to An. Coded sequence B is transmitted. At receiver end due to noise sequence R is obtained. Than we will calculate P(Ai/R) for i = 1 to n. Decoded sequence A for which the probability is maximum is decoded maximum likelihood sequence.
Since there are 2 outcomes for a coin toss, and you will toss the coin 3 times the number of outcomes are 23 or 8. Since H-T-H can occur only 1 way, the probability of the H-T-H sequence is 1/8.
There are no s's in a standard deck of cards, so the probability of selecting any s's, in any sequence of draws, in any strategy of replacement is exactly zero.
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.
The probability of a specific sequence of six consecutive decimal digits occurring early in the decimal representation of pi is usually only about 0. 08% (or more precisely, about 0. 0762%). However, if the sequence can overlap itself (such as 123123 or 999999) then the probability is less. The Feynman point is the first occurrence of four and five consecutive identical digits, but not six.