How would I solve the following: A cookie company determines that the probabilit

Question

How would I solve the following: A cookie company determines that the probability that a chocolate cookie has less than 10 chips is .04. A) if a package of cookies contains 12 cookies, what is the probability that at least one cookie in the package has less than 10 chips? B) if one buys 4 packages of cookies, what is the probability that at least one package has at least one cookie with less than 10 chips?
Thank you :) How would I solve the following: A cookie company determines that the probability that a chocolate cookie has less than 10 chips is .04. A) if a package of cookies contains 12 cookies, what is the probability that at least one cookie in the package has less than 10 chips? B) if one buys 4 packages of cookies, what is the probability that at least one package has at least one cookie with less than 10 chips?
Thank you :) A cookie company determines that the probability that a chocolate cookie has less than 10 chips is .04. A) if a package of cookies contains 12 cookies, what is the probability that at least one cookie in the package has less than 10 chips? B) if one buys 4 packages of cookies, what is the probability that at least one package has at least one cookie with less than 10 chips?
Thank you :)

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
P( X < 1) = P(X=0)
= ( 12 0 ) * 0.04^0 * ( 1- 0.04 ) ^12
= 0.6127
P( X > = 1 ) = 1 - P( X < 1) = 0.3873

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