Homework SourseHow would I solve the following A cookie company determines
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 :)
Solution
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
