toss a coin 20 times and note down the number of heads obtained.calculate the probability of obtaining a head?

Answer 1

50% for head
and 50% for tails!

Answer 2

Either you are being asked to do this experiment or you have not clearly explained the question at hand. What I expect you are going to end up doing is:

Let X be the number of heads in 20 tosses of a fair coin. X has the binomial distribution with n = 20 trials and success probability p = 0.5

In general, if X has the binomial distribution with n trials and a success probability of p then
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[X = x] = 0 for any other value of x.

this is found by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.
Or, to be more accurate, the binomial is the sum of n independent and identically distributed Bernoulli trials.

the mean of the binomial distribution is n * p
the variance of the binomial distribution is n * p * (1 - p)

P(X = 0 ) = 9.536743e-07
P(X = 1 ) = 1.907349e-05
P(X = 2 ) = 0.0001811981
P(X = 3 ) = 0.001087189
P(X = 4 ) = 0.004620552
P(X = 5 ) = 0.01478577
P(X = 6 ) = 0.03696442
P(X = 7 ) = 0.07392883
P(X = 8 ) = 0.1201344
P(X = 9 ) = 0.1601791
P(X = 10 ) = 0.1761971
P(X = 11 ) = 0.1601791
P(X = 12 ) = 0.1201344
P(X = 13 ) = 0.07392883
P(X = 14 ) = 0.03696442
P(X = 15 ) = 0.01478577
P(X = 16 ) = 0.004620552
P(X = 17 ) = 0.001087189
P(X = 18 ) = 0.0001811981
P(X = 19 ) = 1.907349e-05
P(X = 20 ) = 9.536743e-07

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say you toss the coin 20 and count 13 heads. you estimate p as 13/20 and if X ~ Binomial( n = 20, p = 13/20) then:

P(X = 0 ) = 7.609584e-10
P(X = 1 ) = 2.826417e-08
P(X = 2 ) = 4.986607e-07
P(X = 3 ) = 5.556505e-06
P(X = 4 ) = 4.38567e-05
P(X = 5 ) = 0.0002606341
P(X = 6 ) = 0.001210087
P(X = 7 ) = 0.004494608
P(X = 8 ) = 0.01356409
P(X = 9 ) = 0.03358726
P(X = 10 ) = 0.06861397
P(X = 11 ) = 0.1158418
P(X = 12 ) = 0.1613510
P(X = 13 ) = 0.1844012
P(X = 14 ) = 0.1712297
P(X = 15 ) = 0.1271992
P(X = 16 ) = 0.07382096
P(X = 17 ) = 0.03225790
P(X = 18 ) = 0.009984587
P(X = 19 ) = 0.001951874
P(X = 20 ) = 0.0001812455

Answer 3

P (head) = 1/2

Answer 4

P=0.5 for each event.