Question

Assignment 1

Fundamentals of Probability



11. A basket contains 34 heads of lettuce, 5 of which are spoiled. If a sample of 2 is drawn and not replaced, what is the probability that both will be spoiled?


13. A small model-airplane motor has four starting components: key, battery, wire, and glow plug. What is the probability that the system will work if the probability that each component will work is as follows: key (0.998), battery (0.997), wire (0.999), and plug (0.995)?


34. Using the binomial distribution, find the probability of obtaining 2 or less nonconforming restaurants in a sample of 9 when the lot is 15% nonconforming.


42. A sample of 3 medicine bottles is taken from an injection molding machine that is 10% nonconforming. What is the probability of 1 nonconforming medicine bottle in the sample?

Answer 1

11. A basket contains 34 heads of lettuce, 5 of which are spoiled. If a sample of 2 is drawn and not replaced, what is the probability that both will be spoiled?

when the first sample is drawn
then the prob of spoiled lettuce is

5/34

when the seconf sample is drawn , 1 spoiled lettuce is reduced as we are not replacing

so this time the prob is
4/33

so the required probabilty is

5/34 * 4/33 = 0.0178

13. A small model-airplane motor has four starting components: key, battery, wire, and glow plug. What is the probability that the system will work if the probability that each component will work is as follows: key (0.998), battery (0.997), wire (0.999), and plug (0.995)?

the system will work when all the components are working

key (0.998), battery (0.997), wire (0.999), and plug (0.995)

so the required probability is the multiplication of the given probability for each component

0.998 * 0.997* 0.999 *0.995 = 0.9890

Please note that we can answer onyl 1 question at a time , as per the answering guidelines . I have answered 2