A poll is given, showing 40% are in favor of a new building project. If 5 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

the probability that exactly 4 of them favor the new building project is 0.0768

Step-by-step explanation:

We would assume a binomial distribution for the number of people that are in favor of a new building project. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 40% = 40/100 = 0.4

q = 1 - p = 1 - 0.4

q = 0.6

n = 5

x = r = 4

Therefore,

P(x = 4) = 5C4 × 0.4^4 × 0.6^(5 - 4)

P(x = 4) = 5 × 0.0256 × 0.6

P(x = 4) = 0.0768

goog may have it for you

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.