Determine the probability , Mathematics

Assignment Help:

A medical survey was conducted in order to establish the proportion of the population which was infected along with cancer. The results indicated that 40 percent of the population was suffering from the disease.

A sample of 6 people was later taken and examined for the disease. Determine the probability that the given outcomes were observed

a) Merely one person had the disease

b) Exactly two people had the disease

c) Mostly two people had the disease

d) At least two people had the disease

e) Three or four(4) people had the disease

Solution

P(a persona having cancer) = 40%  = 0.4 = P

P(a person not having cancer) = 60%             = 0.6 = 1 - p = q

a)      P(only one person having cancer)     

= 6C1 (0.4)(0.6)5

=  6!/(5! 1!)(0.4)1(0.6)5                      

= 0.1866

Note that from the formula

nCrprqn-r:           where as: n = sample size = 6

                                    p = 0.4

                                    r = 1 = simply one person having cancer

b)      P(2 people had the disease)

= 6C2 (0.4)2 (0.6)4

6!/(6! 2!)=  (0.4)2 (0.6)5

(6 * 5 * 4!)/(4! * 2 *1)=   (0.4)2 (0.6)5

= 15 × (0.4)2 (0.6)5

= 0.311

c)      P(at most 2) = P(0) + P(1) + P(2) = P(0) or P(1) or P(2)

So we estimate the probability of each and add them up.

P(0) = P(nobody having cancer)

= 6C0 (0.4)0(0.6)6

6!/(0! 6!)=  (0.4)0(0.6)6

= (0.6)6

 = 0.0467

The probabilities of P(1) and P(2) have been worked out in part (a) and

Hence P(at most 2) = 0.0467 + 0.1866 + 0.311 = 0.5443

d)      P(at least 2)

            = P(2) + P(3) + P(4) + P(5) + P(6)

= 1 - [P(0) + P(1)] it is a shorter way of working out the solution as

[P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1]

= 1 - (0.0467 + 0.1866)

= 0.7667

e)      P(3 or 4 people had the disease)

= P(3) +P(4)

= 6C3(0.4)3(0.6)3  + 6C4(0.4)4(0.6)2

= ( 6!/(3! 3!)) (0.4)3(0.6)3 + (6!/(2! 4!)) (0.4)4(0.6)2

 = {(6 × 5 × 4 × 3!)/ (3 × 2 × 1 × 3!)}(0.4)3(0.6)3 + {(6 × 5 × 4!)/(2 × 1 × 4!)}  (0.4)4(0.6)2

 = 20(0.4)3(0.6)3  + 15(0.4)4(0.6)2 

= (20 × 0.013824) + (15 × 0.009216)

= 0.27648 + 0.13824

 = 0.41472


Related Discussions:- Determine the probability

Example of distributive law, Maya gives the children examples of distributi...

Maya gives the children examples of distributive with small numbers initially, and leads them towards discovering the law. The usual way she does this is to give the children probl

Function and relation, how to know if it is function and if is relation

how to know if it is function and if is relation

Parametric curve - parametric equations & polar coordinates, Parametric Cur...

Parametric Curve - Parametric Equations & Polar Coordinates Here now, let us take a look at just how we could probably get two tangents lines at a point.  This was surely not

Numerical method, The Stefan-Boltzmann law can be employed to estimate the ...

The Stefan-Boltzmann law can be employed to estimate the rate of radiation of energy H from a surface of copper sphere with radius = 0.15 ±0.01 m, as in H=AesT^4 where H is in watt

Brahmaguptas problem, How to solve Brahmaguptas Problem? Explain Brahmagupt...

How to solve Brahmaguptas Problem? Explain Brahmaguptas Problem solving method?

Applications of integrals, Applications of Integrals In this part we're...

Applications of Integrals In this part we're going to come across at some of the applications of integration.  It should be noted also that these kinds of applications are illu

Find a general solution to the differential equation, Example: Find a gene...

Example: Find a general solution to the subsequent differential equation. 2 y′′ + 18 y + 6 tan (3t) Solution First, as the formula for variation of parameters needs coe

On income and return from shares, a company declares a semu annual dividend...

a company declares a semu annual dividend on 5%.a man has 400 shares of the company.if his annual income from the share is rs 1000 find the face value of each share?

Concepts, what are core concepts of marketing?

what are core concepts of marketing?

Data editing, how to remove wild points in a data set...

how to remove wild points in a data set...

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