1/2 or 5/10
7*(1/2)7 = 7/128 = 5.47% approx.
5/216
four out of seven times
It is 6/36 = 1/6.
3/10 or 0.3
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.
The probability would be once in 128 attempts. You don't have to toss seven coins simultaneously. the 7 tosses just have to be independent of one another.
That's the same as the total probability (1) minus the probability of seven heads. So: 1 - (1/2)7 = 127/128
The probability of getting only one tails is (1/2)7. With seven permutations of which flip is the tails, this gives a probability of: P(six heads in seven flips) = 7*(1/2)7 = 7/128
The probability of one event or the other occurring is the probability of one plus the probability of the other. The probability of getting 3 heads is the probability of 3 heads (1/23) multiplied by the probability of 4 tails (1/24) multiplied by the number of possible ways this could happen. This is 7c3 or 35. Thus the probability of 3 heads is 0.2734375. The probability of 2 tails is the probability of 2 tails (1/22) multiplied by the probability of 5 heads (1/25) multiplied by the number of ways this could happen. That is 7c5 or 21. Thus the probability of 2 tails is 0.1640625 The probability of one or the other is the sum of their probabilities: 0.1640625 + 0.2734375 = 0.4375 Thus the probability of getting 3 heads or 2 tails is 0.4375.
It is 1/2^7 = 1/128.
Experimental probability is the number of times some particular outcome occurred divided by the number of trials conducted. For instance, if you threw a coin ten times and got heads seven times, you could say that the experimental probability of heads was 0.7. Contrast this with theoretical probability, which is the (infinitely) long term probability that something will happen a certain way. The theoretical probability of throwing heads on a fair coin, for instance, is 0.5, but the experimental probability will only come close to that if you conduct a large number of trials.
The probability of obtaining 7 heads in eight flips of a coin is:P(7H) = 8(1/2)8 = 0.03125 = 3.1%
7*(1/2)7 = 7/128 = 5.47% approx.
Mr. Palmer moved to Canada in 1974 where he continued to teach and write. He died there on June 16, 2013. Related Documents.
Empirical means by observation, so empirical probability, or experimental probability, is the probability that is observed in a set of trials. For example, if you flip a coin ten times and get seven heads, your empirical probability is 7 in 10. This is different than the theoretical probability, which for a fair coin is 5 in 10, but that result will only be approximated by the empirical results, and then only with a larger number of trials.
0% probability