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The binom.pmf() method from the scipy.stats library can be used to calculate the PMF of the binomial distribution at any value. This method takes 3 values:

  • x: the value of interest
  • n: the number of trials
  • p: the probability of success

For example, suppose we flip a fair coin 10 times and count the number of heads. We can use the binom.pmf() function to calculate the probability of observing 6 heads as follows:

# import necessary library
import scipy.stats as stats

# st.binom.pmf(x, n, p)
print(stats.binom.pmf(6, 10, 0.5))

Output:

# 0.205078

Notice that two of the three values that go into the stats.binomial.pmf() method are the parameters that define the binomial distribution: n represents the number of trials and p represents the probability of success.

Instructions

1.

Change the scaffolded code to calculate the probability of observing 3 heads in 10 fair coin flips. Save this probability to prob_1.

Update x and n in script.py accordingly.

2.

Using the same logic in question 1, calculate prob_2 to be the probability of observing 7 heads out of 20 fair coin flips. However, this time, directly input values into the stats.binomial.pmf() method.

Then print prob_2.

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