I got this problem in my book.. I will directly go the last part which I could not solve. P(good condition)=0.91854, P(bad condition)=0.08146. A random package check is checked by a company till there is a package in a bad condition . 1. What is the probability that the company will check exactly 4 packages? 2. it is known that the first 3 packages that were checked are in good condition , what is the probability that more than 8 packages will be checked(edit: the answer should be 0.654).

pilinyir1 2022-09-24 Answered
Geometric distribution and Conditional probability problem
I got this problem in my book.. I will directly go the last part which I could not solve.
P ( g o o d c o n d i t i o n ) = 0.91854
P ( b a d c o n d i t i o n ) = 0.08146
a random package check is checked by a company till there is a package in a bad condition .
1. What is the probability that the company will check exactly 4 packages?
2. It is known that the first 3 packages that were checked are in good condition , what is the probability that more than 8 packages will be checked(edit: the answer should be 0.654).
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

tal1ell0s
Answered 2022-09-25 Author has 6 answers
Step 1
P ( X > 5 ) = 1 P ( X 5 ) = 0.91854 5 0.6539
To calculate it you can use the fact that the CDF of your rv is known...
Step 2
If you do not know the CDF of a geometric distribution you can do the following reasoning...the probability to have more than 5 failures is exactly the probability of having 5 consecutive failures...after this events any event can happen....thus you probability is 0.91854 × 0.91854 × 0.91854 × 0.91854 × 0.91854 × 1 0.654
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-08-13
Probability of a triangle inside a square
If we have the square with vertices at the 4 corners of ( 0 , 1 ) 2 , and we choose a random point z inside the square, the triangle is between (0,0), (1,0) and z, what is the CDF and PDF of the random variable A T representing the area of the triangle?
asked 2022-10-22
Suppose that X and Y are independent geometric random variables with the same parameter P. Find the value and verify:
P ( X = i | X + Y = n )
My initial reaction is that since they are independent and have the same parameter P, that the given is not necessary and the answer would just end up being ( 1 P ) ( i 1 ) P but I am pretty sure that I am missing something, can someone help me get started on this proof?
asked 2022-08-12
Geometric probabilities solution verification
An unbiased coin is tossed until a head appears and then tossed until a tail appears. If the tosses are independent, what is the probability that a total of exactly n tosses will be required?
My attempt:
P(n tosses required to produce one head and one tail) = P ( x tosses needed for first head ) × P ( y tosses needed for first tail ) where   x + y = n .
So, the probability becomes ( 1 2 ) x 1 ( 1 2 ) ( 1 2 ) y 1 ( 1 2 ) = ( 1 2 ) n .
This is not the correct answer, however. The correct answer is ( 1 2 ) n ( n 1 ). Can someone pleas explain what I did incorrectly and where the n 1 factor is coming from?
asked 2022-07-16
When A and B flip coins, the one coming closest to a given line wins 1 penny from the other. If A starts with 3 and B with 7 pennies, what is the probability that A winds up with all of the money if both players are equally skilled? What if A were a better player who won 60% percent of the time?
asked 2022-10-12
Probability of 3 numbers chosen between 0 and 10 being within 1 of each other
I was trying to find the probability that 3 real numbers uniformly chosen from 0 to 10 are within 1 of each other (the largest number minus the smallest number is at most 1).
I tried using geometric probability, and I got a region that looks like what you would get if you put one vertex of a unit cube at the origin (and orient the edges such that they line up with the positive axes), and move the corner at the origin from (0,0,0) to (9,9,9) (is this region correct?). I calculated the volume by finding the area of the one of the faces of the cube (which is 1), and multiplying it by the distance it moved (which is 9). Since there are three of these squares, the volume is 27. I then add this to the volume of the cube, which results in 28. The total volume is 10 3 = 1000, so the probability is 28 / 1000 = 7 / 250.
asked 2022-08-16
Conditional expectation of a uniform distribution given a geometric distribution
Let N follow a geometric distribution with probability p. After the success of the experiment we define X, a uniform distribution from 1 to N. Both distributions are discrete. Find E[X|N].
asked 2022-07-22
Find the probability that a geometric random variable X is an even number
Let α be the probability that a geometric random variable X with parameter p is an even number
a) Find α using the identity α = i = 1 P [ X = 2 i ].
b)Find α by conditioning on wether X = 1 or X > 1

New questions