Statistics Question Help

Question

33% of all pets sold at a pet store are dogs. One day, 9 people arrive at the store and purchase pets. (Note: One pet is purchased per person.)

(a) What is the probability that exactly 3 of them are dogs?

(b) If the store has only 5 dogs, what is the probability that they have sufficient dogs for sale that day?

Answer 1

p = probability of pets that are dogs

n = 9 people (sample size)

x = # of people bought dogs

P(X = 3) = C(9,3)*(0.33)³(0.67)⁶ = 0.2731

The probability that exactly 3 pets are dogs is about 0.2731.

P(X ≤ 5) = C(9,0)*(0.33)⁰(0.67)⁹ + C(9,1)*(0.33)¹(0.67)⁸ + C(9,2)*(0.33)²(0.67)⁷ + C(9,3)*(0.33)³(0.67)⁶ + C(9,4)*(0.33)⁴(0.67)⁵ + C(9,5)*(0.33)⁵(0.67)⁴ ≈ 0.96

The probability that up to 5 dogs are sold at the store is about 0.96.