An extensive study undertaken by the national highway

Question

Question: An extensive study undertaken by the National Highway Traffic Safety Administration reported that 17% of children between the ages of five and six use no seat belt, 29% use a seat belt, and 54% use a child seat. In a sample of 15 children between five and six let N₁, N₂, N₃ be the number of children using no seat belt, a seat belt, and a child seat, respectively.

(a) Find the probability that exactly 10 children use a child seat.

(b) Find the probability that exactly 10 children use a child seat and five use a seat belt.

(c) Find Var(N₂ + N₃) and Cov(N₁, N₂ + N₃).