Question

Your task is to complete a function "count_heads()" that takes two inputs N and R. The function should return the probability of getting exactly R heads on N successive tosses of a fair coin. A fair coin has equal probability of landing a head or a tail (i.e. 0.5) on each toss. For example, for the arguments provided as follows

Sample Input :

1 1

Sample Output :

0.500000

Sample Input :

4 3

Sample Output :

0.250000​

Answer 1

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Answer 2

Answer: Output  0.250000

Explanation: The probability of getting K heads in N coin tosses can be calculated using the below formula of binomial distribution of probability:

        $^{n}C_{k}$ ×  $p^{k}$× $q^{n-k}$

Where p = probability of getting head and

            q = probability of getting tail.

             p and q both are $\frac{1}{2}$.

So the equation becomes $[\frac{1}{2^n} * \frac{n!}{ r! * (n-r)!}]$

As of now, by the implementation of the above approach by python,

def fact(n):

res = 1

for i in range(2, n + 1):

 res = res * i

return res

# Applying the formula

def count_heads(n, r):

output = fact(n) / (fact(r) * fact(n - r))

output = output / (pow(2, n))

return output

# Driver code

n = 4

r = 3

# Call count_heads with n and r

print (count_heads(n, r))

As Output is 0.250000

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