if six coins are tossed, what is the probability at least one head appear?
richmorichmo
17 Oct, 2019
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What is the probability of getting at least one heads? ... What is the probability of getting at least 3 heads if a fair coin is tossed 6 times? ... When 6 coins are tossed at a time; total number of possible outcomes = (2*2*2*2*2*2) = 2^6 = 64
if six coins are tossed at a time the probability of getting a head at a time
the possible outcome include the following: 1/2*1/2*1/2*1/2*1/2*1/2=1/64 since each coin has two faces a head or a tail.
Sample space:
|(H,H,H,H,H,H) (T,T,T,T,T,T) |
|(H,H,H,H,H,T) (T,T,T,T,T,H) |
|(H,H,H,H,T,T) (T,T,T,T,H,H) |
|(H,H,H,T,T,T) (T,T,T,H,H,H) | × 5 (№ of sample
|(H,H,T,T,T,T) (T,T,H,H,H,H) | space= 12×5
|(H,T,T,T,T,T) (T,H,H,H,H,H) | = 60)
|(H,H,H,H,H,H)|
|(H,H,H,H,H,T)|
|(H,H,H,H,T,T)| ×1 (№ of sample space=4×1= 4)
|(H,H,H,T,T,T)|
Total number of sample space= 64
In the above section with a (×5) attached, it means that there is a possibility for that first 12 sample space sequence to appear five times which will amount to a 60th sample space.
And the section with the (×1) attached, it means that after the fifth sequence, there is a continuation to make up a 64th sample space, which is the total number of possible outcome.
Now, in every of the first 12 possible sample space, excluding the last 4 sample spaces above, it will be observed that (T,T,T,T,T,T) will appear five(5) times, reducing the № of required outcome of at least one head appearing to a (64 - 5)= 59.
And '...at least one head appears...' means that one or more head must appear in the 64 possible sample spaces from the tossed six coins.
As a result, the № of required outcome for at least one head to appear is 59.
Therefore, the probability(at least one head appears)= № of required outcome/№ of possible outcome= 59/64.
Thank you for your understanding.
The correct answer is 63/64
n(s) = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64
The 1/2 was gotten from the probability of 1 fair coin times six because there are six coins.
n(Pr) = 1-(1/64)
= 63/64
Thanks for your understanding
