Create a binomial probability experiment with the data from the public opinion poll experiment. Use the probability of success and failure from the experiment. Calculate the probability of the number of successes in 100 random tests. For example, if the probability of success is 0.20 and the number of trials is 100, then the number of successes is 20.

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"Binomial probability distribution is the representation of a probability with only two outcomes success and failure under given number of trials."

Formula used

Binomial probability distribution is given by

[tex]\\n{C}_{x}p^{x}q^{n-x}[/tex]

n= number of experiments

x = 0, 1, 2, 3,.......

p = probability of success

q = probability of failure

According to the question,

Number of trials 'n' = 100

Probability of success 'p' = (20 / 100)

= 0.20

Probability of failure 'q' = 1 - p

= 1 - (20/100)

= (80 / 100)

Substitute the value in the formula we get

Required probability = [tex]\ 100C_{x[/tex][tex]( 0.20)^{x} (0.80)^{100-x}[/tex]

Example:

Tossing a coin 6 times getting exactly two heads.

Number of trials 'n' = 6

Number of heads 'x' =2

Only two possible outcomes head or tail

Probability of getting head 'p' = 1 / 2

Probability of not getting head 'q' = 1 /2

Required probability = [tex]\ 6C_{2[/tex] (1/2)²(1/2) ⁶⁻²

=[tex]\ 6C_{2[/tex] (1/2)⁶

Hence, binomial probability distribution for the given set of data is

[tex]\ 100C_{x[/tex][tex]( 0.20)^{x} (0.80)^{100-x}[/tex]

Learn more about binomial probability distribution here

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