Question

An experiment consists of recording boy-girl composition of families with 2 children. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?

Name: Problem 8, Chapter 16: NCERT Class 11 - Math
Uploaded: 2021-06-07T06:54:53-08:00
Duration: 1 min 2 s
Channel: Aman Gupta
Description: An experiment consists of recording boy-girl composition of families with 2 children. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?

   An experiment consists of recording boy-girl composition of families with 2 children.
(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?

NCERT Class 11 - Math

Parvin Sinclair,… 2011 Edition

Chapter 16, Problem 8

Instant Answer

Solved by Expert Aman Gupta

06/07/2021

Step 1

The possible outcomes are: both children are girls (GG), the first child is a girl and the second is a boy (GB), the first child is a boy and the second is a girl (BG), or both children are boys (BB). Therefore, the sample space is: \[ S_1 = \{GG, GB, BG, BB\} \] Show more…

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An experiment consists of recording boy-girl composition of families with 2 children. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?

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Key Concepts

Sample Space

The sample space in probability refers to the complete set of all possible outcomes of an experiment. It is a fundamental concept that helps in defining probabilities by listing each potential result that could occur under the conditions of the experiment.

Ordered Outcomes

When the order of events matters, each outcome is represented as an ordered tuple. This concept is used when the sequence in which events occur provides additional information, such as the order of births or sequential results.

Aggregation of Outcomes

Aggregation of outcomes refers to grouping or classifying results based on specific criteria rather than their sequence. For example, counting the number of girls in a family involves aggregating the outcomes irrespective of the order in which they appear.

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