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

Confidence interval, Confidence Interval The interval estimate or a 'co...

Confidence Interval The interval estimate or a 'confidence interval' consists of a range as an upper confidence limit and lower confidence limit whether we are confident that a

What is slope of a line, What is Slope of a Line ? A line can have a "...

What is Slope of a Line ? A line can have a "steep" slope or a "gradual" slope. slope = rise/run The "rise" is the distance going up or down. The "run" is the distance goin

Trigonometry.., if b+c=3a then the value of cotB/2.cotC/2 is equal to

if b+c=3a then the value of cotB/2.cotC/2 is equal to

#title.heat loss in a cylindrical pipe., briefly explain how the famous equ...

briefly explain how the famous equation for the loss of heat in a cylindrical pipe is derived

Quotient rule (f/g)'' = (f''g - fg'')/g2, Quotient Rule (f/g)' = (f'g - ...

Quotient Rule (f/g)' = (f'g - fg')/g 2 Here, we can do this by using the definition of the derivative or along with Logarithmic Definition. Proof Here we do the pr

Negative skewness-measure of central tendency, Negative Skewness It i...

Negative Skewness It is an asymmetrical curve whether the long tail extends to the left NB: In developed countries this frequency curve for the age distribution is charact

What is trigonometric ratios, What is Trigonometric Ratios ? Trigonome...

What is Trigonometric Ratios ? Trigonometry, a branch of mathematics, is based on the ratios known as sine, cosine, and tangent. Trigonometric ratios apply only to right trian

Geometric progression (g.p.), Learning geometric progression ...

Learning geometric progression vis-á-vis arithmetic progression should make it easier. In geometric progression also we denote the first t

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