The binomial distribution fits the case of n independent events each one with a probability of success equal to p where k successes have been achieved.
The PMF (Probability Mass Function) of the binomial distribution is
Where
The individual probability that an electronic device does not function properly is p=0.1. We know n=10 devices have been bought and we want to compute the probability that 7 devices function properly. Please notice that this is not the value of k since p is the probability of failure. The correct value of k=10-7=3. The required probability is
Cos (π/2 - x) = sin x = 3/5 tan x = sin x / cos x = 3/5 / 4/5 = 3/4 csc x = 1/sin x = 1 / 3/5 = 5/3 sec x = 1/cos x = 1 / 4/5 = 5/4 cot x = 1/tan x = 1 / 3/4 = 4/3.