http://www.ck12.org Chapter 4. Probability Distributions
Guided Practice
You have a summer job at a jelly bean factory as a quality control clerk. Your job is to ensure that the jelly beans
coming through the line are the right size and shape. The probability that any particular shipment of jelly beans
passes inspection is 90%. A normal day at the jelly bean factory means 15 shipments are produced. What is the
probability that exactly 10 will pass inspection?
Answer:
There are 15 shipments, son=15.
A success is a shipment passing inspection, and we are interested inexactly10 passing inspection.
Therefore,a=10.
The probability of a success is 90%, or 0.90, and, thus,p= 0 .90.
Therefore, the probability of a failure is 1− 0 .90, or 0.10. From this, you know thatq= 0 .10.
P(X=a) =nCa×pa×q(n−a)
P(10 shipments passing) = 15 C 10 ×p^10 ×q^5
P(10 shipments passing) = 15 C 10 ×( 0. 90 )^10 ×( 0. 10 )^5
P(10 shipments passing) = 3003 × 0. 3487 ×( 1. 00 × 10 −^5 )
P(10 shipments passing) = 0. 0105Therefore, the probability thatexactly10 of the 15 shipments will pass inspection is 1.05%.
Using technology to check, you get the following:
Practice
- It is determined that because of a particular genetic trend in a family, the probability of having a boy is 60%.
Janet and David decide to have 4 children. What is the probability that they will haveexactly2 boys?