(a) An association is made up of 6 farmers and 8 traders. If an executive body of 4 members is to be formed, find the probability that it will consist of at least two farmers. (b) The probability of an accident occurring in a given month in factories X, Y, and Z are \(\frac{1}{5}, \frac{1}{12} \) and \(\frac{1}{6}\) respectively. Find the probability that the accident will occur in: i) none of the factories; (ii) all the factories; (iii) at least one factory.

Wednesday, 09 April 2025

Register • Login

(a) An association is made up of 6 farmers and 8 traders. If an executive body of 4 ...

Trending Questions

** Free JAMB 2025 CBT Practice **

In a federal system,the essence of specifying the constitutional relationship between ...

Abraham circumcised his son,Isaac, on the eight days because

In mammals, the exchange of nutrients and metabolic products occurs in the

The problems of conducting census include?

Take Free Practice Test On 2025 JAMB UTME, Post UTME, WAEC SSCE, GCE, NECO SSCE

(a) An association is made up of 6 farmers and 8 traders. If an executive body of 4 members is to be formed, find the probability that it will consist of at least two farmers. (b) The probability of an accident occurring in a given month in factories X, Y, and Z are

\frac{1}{5}, \frac{1}{12}

and

\frac{1}{6}

respectively.
Find the probability that the accident will occur in:
i) none of the factories;
(ii) all the factories;
(iii) at least one factory.

Explanation

No. of farmers = 6
No. of traders = 8
Total = 14
Pr(at least two farmers)
=

\frac{^{6} C_{2} \times^{8} C_{2}}{^{14} C_{4}} + \frac{^{6} C_{3} \times^{8} C_{1}}{^{14}} + \frac{^{6} C_{4} \times^{8} C_{0}}{^{14} C_{4}}

\frac{15 \times 28}{1001} + \frac{20 \times 8}{1001} + \frac{15 \times 1}{1001}

\frac{420}{1001} + \frac{160}{1001} + \frac{15}{1001}

\frac{420 + 160 + 15}{1001}

\frac{595}{1001}

(b) P(x) =

\frac{1}{5}

p(x

^{1}

) = 1 -

\frac{1}{5}

\frac{4}{5}

p(y) =

\frac{1}{2}

, p(y

^{1}

)
= 1 -

\frac{1}{12}

\frac{11}{12}

p(2) =

\frac{1}{6}

p(z

^{1}

) = 1 -

\frac{1}{6}

\frac{5}{6}

(i) Pr(None)
=

\frac{4}{5} \times \frac{11}{12} \times \frac{5}{6} = \frac{11}{18}

(ii) Pr(all the factories)
=

\frac{1}{5} \times \frac{1}{12} \times \frac{1}{6} = \frac{1}{360^{o}}

(iii) Pr (at least one factory)
= 1 - Pr (none) =

\frac{1}{1} - \frac{11}{18}

\frac{18 - 11}{18}

\frac{7}{18}

Prev Current Next

STAY UPDATED
FOLLOW US ON :

Facebook

Subjects

• Accounts - Principles of Accounts

• Animal Husbandry

• Agricultural Science

• Arabic

• Biology

• Book Keeping

• Chemistry

• Commerce

• Christian Religious Knowledge (CRK)

• Civic Education

• Catering Craft Practice

• Computer Studies

• Data Processing

• English language

• Economics

• Fine Arts

• French

• Further Mathematics

• Geography

• Government

• History

• Hausa

• Home Economics

• Insurance

• Igbo

• Islamic Religious Knowledge (IRK)

• Literature in English

• Music

• Marketing

• Mathematics

• Physics

• Yoruba

About

Back to Top

...

Disclaimer

All Views, Names, Acronyms, Trademarks, Expressed on this website are those of their respective owners. Please note that www.schoolngr.com is not affiliated with any of the institutions featured in this website. It is always recommended to visit an institutions or sources official website for more information. In the same vein, all comments placed here do not represent the opinion of schoolngr.com