Q3. Suppose three students of NSU named A, B and C are going to sit their spring semester final exam in May-2021. Each of the three students can be promoted to the next semester as either with scholarship (1) or without scholarship (0). With the notation (0, 1, 0) used to represent the situation where student B is awarded scholarship but students A and C are not awarded scholarship. The probabilities that the three students A, B and C get a scholarship in an examination are, respectively. P(A = 1) = 0.1, P(B = 1) = 0.2 and P(C = 1) =0.3, and three outcomes are independent. (i) Write down the all possible combination of students' scholarship status (sample space). (ii) Calculate the probability that all three students will be awarded a scholarship together i.e. P(A = 1, B = 1, C= 1) = P(1, 1, 1). (iii) Calculate the probability that only student C will be awarded scholarship.

Q3. Suppose three students of NSU named A, B and C are going to sit their spring semester final exam in May-2021. Each of the three students can be promoted to the next semester as either with scholarship (1) or without scholarship (0). With the notation (0, 1, 0) used to represent the situation where student B is awarded scholarship but students A and C are not awarded scholarship. The probabilities that the three students A, B and C get a scholarship in an examination are, respectively. P(A = 1) = 0.1, P(B = 1) = 0.2 and P(C = 1) =0.3, and three outcomes are independent. (i) Write down the all possible combination of students' scholarship status (sample space). (ii) Calculate the probability that all three students will be awarded a scholarship together i.e. P(A = 1, B = 1, C= 1) = P(1, 1, 1). (iii) Calculate the probability that only student C will be awarded scholarship.

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Description: Q3. Suppose three students of NSU named A, B and C are going to sit their spring semester final exam inMay-2021. Each of the three students can be promoted to the next semester as either with scholarship (1)or without scholarship (0). With the notat

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Q3. Suppose three students of NSU named A, B and C are going to sit their spring semester final exam in
May-2021. Each of the three students can be promoted to the next semester as either with scholarship (1)
or without scholarship (0). With the notation (0, 1, 0) used to represent the situation where student B is
awarded scholarship but students A and C are not awarded scholarship. The probabilities that the three
students A, B and C get a scholarship in an examination are, respectively, P(A = 1) = 0.1, P(B = 1) =
0.2 and P(C = 1) =0.3, and three outcomes are independent.
(i)
Write down the all possible combination of students' scholarship status (sample space).
(ii)
Calculate the probability that all three students will be awarded a scholarship together i.e.
P(A = 1, B = 1, C = 1) = P(1, 1, 1).
(iii)
Calculate the probability that only student C will be awarded scholarship.
(iv)
Calculate the probability that only one student will be awarded scholarship.
(v)
Given that only one student gets a scholarship, find the probability that it was candidate C

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