From Past Experience, It Is Known 90% of One-Year-Old Children

Essay

From past experience, it is known 90% of one-year-old children can distinguish their mother's voice from the voice of a similar-sounding female. A random sample of 20 one-year-olds are given this voice recognition test.
a. Find the probability that at least three children do not recognize their mother's voice.
b. Find the probability that all 20 children recognize their mother's voice.
c. Let the random variable x denote the number of children who do not recognize their mother's voice. Find the mean of x.
d. Let the random variable x denote the number of children who do not recognize their mother's voice. Find the variance of x.
e. Find the probability that, at most, four children do not recognize their mother's voice.