This document presents a probability case study involving two friends, A and B, applying for two vacancies with different probabilities of selection. The probabilities of A and B being selected are 1/4 and 1/5, respectively. The document calculates the probabilities of: (1) one of them being selected; (2) both being selected; (3) neither being selected; and (4) at least one being selected. It concludes by asking students to solve the case study on probability.

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Unit No.5.
PROBABILITY
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean, EDP & Associate Professor MBA
1
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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302-DECISION SCIENCE
Unit No.5. Probability
5.9 Case 6: Probability
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean EDP & Associate Professor MBA
2
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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NETWORK ANALYSIS
 At the End of the Session Student will be able to
understand-
A. Case 6: Probability

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Probability
Two Friends A & B apply for two vacancies at the same
post. The probabilities of their selection are ¼ and 1/5
respectively. What is the chance that-
i. One of them will be selected,
ii. Both will be selected,
iii. None will be selected,
iv. At least one will be selected.

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Probability
Let, A Event that A is selected
B Event that B is selected
𝑃 𝐴 =
𝑚
𝑛
=
1
4
𝑎𝑛𝑑 𝑃 𝐵 =
𝑚
𝑛
=
1
5
𝑃 𝐴 𝑛𝑜𝑡 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 = 𝑃(𝐴) = 1 −
1
4
=
3
4
𝑃 𝐵 𝑛𝑜𝑡 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 = 𝑃(𝐵) = 1 −
1
5
=
4
5

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Probability
i) Now if only one is selected i.e. (A is selected and B is
not) or (B is selected and A is not)
= P(AՈB) + P(BՈA)
= P 𝐴 . 𝑃 𝐵 + P 𝐵 . 𝑃 𝐴
=
1
4
.
4
5
+
1
5
.
3
4
=
4
20
+
3
20
=
7
20
ii) If both are selected, then Required Probability
= P(AՈB)
= P(A).P(B) =
1
4
.
1
5
=
1
20

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Probability
iii) P none of them is selected
= 1- P(at least one is selected)
= 1 - P(One is selected or both are selected)
= 1 −
7
20
+
1
20
= 1 −
8
20
=
12
20
=
3
5
iv) At least one will be selected
= P(One is selected or both are selected)
= P(One is selected) + P(Both are selected)
=
7
20
+
1
20
=
8
20
=
2
5

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EXERCISE
 Solve the Case 6 on Probability.

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For More Details Contact1
Dr. V M Tidake
tidkevishal@gmail.com
tidkevishalmba@sanjivani.org.in