The probability that out of 12 people, only 5 do not cover their mouth when sneezing is: 0.122
How to use Binomial Probability distribution?
The formula for Binomial Probability distribution is:
P(X = x) = ⁿCₓ * pˣ * (1 - p)⁽ⁿ ⁻ ˣ⁾
where:
'x' is the number of successes of the experiment
n is number of trials
p is success probability for each trial at the experiment.
We are given:
p = 0.267
Thus, the probability that out of 12 people, only 5 do not cover their mouth when sneezing is:
P(X = 5) = ¹²C₅ * 0.267⁵ * (1 - 0.267)⁽¹² ⁻ ⁵⁾
P(X = 5) = 0.122