A coin is tossed on 5 occasions .What is the probability that a head will appear on all 5 occasions
The same as the probability that a tail will appear on all five or one head and four tails.
With the toss of a coin, providing the coin toss is guaranteed to produce a truly random result (there are ways to flip a coin, catch it and know what the result will be) then the likelihood that all five flips will return the same results is equally as probably as producing any other combination.
This is because each flip of the coin is independent of the previous flip and cannot therefore influence the following flips.
Nick B has it right.
I think the numbers would be (1/2)^5 --> .03125 or 3.125%.
Or 1/32 (same thing).
Check my math.
For each toss, 2 possible outcomes.
So total possible outcomes for 5 tosses is 2x2x2x2x2=32
All heads is only possible in one way, heads appears in each toss. So the probablity is total number of outcomes for the even over the total number of all outcomes.
So the probablity is 1/32.
Assuming the coin is fair, of course.
The reason that the probability of obtaining 5 heads is the same as the probability of obtaining any other possible combination of heads and tails for the 5 flips is because the probability of heads equals the probability of tails, which is .5
If the two possible outcomes had different probabilities (which is the case in most situations other than coin tosses) then this would not be true, even if each action is independent of the others.
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