The requirement that one coin is a head is superfluous and does not matter.
The simplified question is "what is the probability of obtaining exactly six heads in seven flips of a coin?"...
There are 128 permutations (27) of seven coins, or seven flips of one coin. Of these, there are seven permutations where there are exactly six heads, i.e. where there is only one tail.
The probability, then, of tossing six heads in seven coin tosses is 7 in 128, or 0.0546875.
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The probability of obtaining 7 heads in eight flips of a coin is:P(7H) = 8(1/2)8 = 0.03125 = 3.1%
We can simplify the question by putting it this way: what is the probability that exactly one out of two coin flips is a head? Our options are HH, HT, TH, TT. Two of these four have exactly one head. So 2/4=.5 is the answer.
The probability of a head in one flip is 1/2. The probability of HHHHTT is (1/2)6 = 1/64 The possible correct flips are HHHHTT, HHHTHT, HHTHHT, HTHHHT, THHHHT, HHHTTH, HHTHTH, HTHHTH, THHHTH, HHTTHH, HTHTHH, THHTHH, HTTHHH, THTHHH, TTHHHH, each with a probability of 1/64. Total probability is 15/64.
It is a variable that can take a number of different values. The probability that it takes a value in any given range is determined by a random process and the value of that probability is given by the probability distribution function.It is a variable that can take a number of different values. The probability that it takes a value in any given range is determined by a random process and the value of that probability is given by the probability distribution function.It is a variable that can take a number of different values. The probability that it takes a value in any given range is determined by a random process and the value of that probability is given by the probability distribution function.It is a variable that can take a number of different values. The probability that it takes a value in any given range is determined by a random process and the value of that probability is given by the probability distribution function.
all probabilities smaller than the given probability ("at most") all probabilities larger than the given probability ("at least")