probability, Mathematics

Assignment Help:
Question: There are 6 letters and 6 self addressed envelopes.What is the probability that atleast 1 is placed correctly??

Ans: If we let A be the event that letter A is in the correct envelope, and
similarly B is event that letter B is in the correct envelope, then

P(A) = 1/5

P(A and B) = 1/5 x 1/4

Now use the inclusion, exclusion formula to get the probability that A or
B or C .... or E are correctly placed.

P(A or B or C .... or E) = P(A) + P(B) + P(C) + P(D) + P(E)
- P(A and B) - P(B and C) -....
+ P(A and B and C) + P(B and C and D) + ....
- P(A and B and C and D) - P(...) -......
+ P(A and B and C and D and E)

= 5 x (1/5)
- 5C2 x (1/5)(1/4)
+ 5C3 x (1/5)(1/4)(1/3)
- 5C4 x (1/5)(1/4)(1/3)(1/2)
+ (1/5)(1/4)(1/3)(1/2)(1/1)

5x4 1 5x4x3 1 5x4x3x2 1 1
1 - ---- x ---- + ------ x ----- - --------- x ------- + --------
1x2 5x4 1x2x3 5x4x3 1x2x3x4 5x4x3x2 5x4x3x2x1

= 1 - 1/2! + 1/3! - 1/4! + 1/5!


This is the probability that at least one letter is correctly placed.

Related Discussions:- probability

Estimation of population proportions, Estimation of population proportions ...

Estimation of population proportions This form of estimation applies at the times while information cannot be described as a mean or as a measure but only as a percentage or fr

Nun, how do you identify area ??

how do you identify area ??

The central limit theorem, The Central Limit Theorem  The theories was ...

The Central Limit Theorem  The theories was introduced by De Moivre and according to it; if we choose a large number of simple random samples, says from any population and find

Help me, How should Shoppers’ Stop develop its demand forecasts?

How should Shoppers’ Stop develop its demand forecasts?

Calculate the area and perimeter of a right triangle, Calculate the area an...

Calculate the area and perimeter of a right triangle: Calculate the area and perimeter of a right triangle with a 9" base and sides measuring 12 and 15.  Be sure to involve th

Prove any prime number is irrational, 1. Show that there do not exist integ...

1. Show that there do not exist integers x and y for which 110x + 315y = 12. 2. If a and b are odd integers, prove that a 2 +b 2 is divisible by 2 but is NOT divisible by 4. H

Geometria, un prisma retto ha per base un rombo avente una diagonale lunga ...

un prisma retto ha per base un rombo avente una diagonale lunga 24cm. sapendo che la superficie laterale e quella totale misurano rispettivamente 2800cm e3568cm ,calcola la misura

Solid geomerty, find the equation to the sphere through the circle xsqaure+...

find the equation to the sphere through the circle xsqaure+ysquare+zsquare+=9 , 2x+3y+4z=5

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd