Question

A family has two children. M represents male, and F represents female.

Answer 1

Answer:

Option c) Sample space$=\{\bf FM, FF, MM, MF\}$

Step-by-step explanation:

Given that a family has two children.

Let M represents male, and F represents female.

In probability theory, the sample space (also called sample description space or possibility space) of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set. It is common to refer to a sample space by the labels S, $\Omega$, or  $\cup$(for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols. They can also be finite, countably infinite, or uncountably infinite.

Let S be the sample space of the given data.

Here the sample space is typically the set {male, female}, commonly written $\{M, F\}$

ie, S is the set $\{male, female\}$  or $S=\{M, F\}$

For the gender of the children,  corresponding sample space would be $\{(male,male), (male,female), (female,male), (female,female)\}$ , commonly written as

$\{MM,MF,FM,FF\}$

S is the set $\{(male,male), (male,female), (female,male), (female,female)\}$  or  $S=\{MM,MF,FM,FF\}$