Question

Classwork - Chapter 5 X + apter 5 Submitting an external tool Available Jul 29 at 12am-Jul 29 at 11:59pm 1 day ter 5 Jessica Sa Due in 3 hours, 55 minutes. Due Wed 07/29 A manufacturing machine has a 1% defect rate, If 5 items are chosen at random, what is the probability that at least one will have a defect? Preview Points possible: 1 This is attempt 1 of 3. Submit

Answer 1

GIven :

p = 1 % = 0.01

n = 5

Solution :

As p = 0.01, therefore

q = 1-p = 1 -0.01 = 0.99

This is a binomial probability distribution problem,

$P(x) = \binom{n}{x}p^{x}q^{n-x}$

We have to find the probability that at least one will have a defect

$P(x\geq 1) = 1 - P(x = 0)$

$P(x\geq 1) = 1 - \left ( \binom{5}{0}(0.01)^{0}(0.99)^{5-0} \right )$

$P(x\geq 1) = 1 - 0.951$

$P(x\geq 1) = 0.049$

**Thank you for giving me the opportunity to help you. Please give me thumbs up if you like this answer.**