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Probability

Short Answer Type

361.

Describe the sample space for the following experiment.
A coin is tossed twice.

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362. Describe the sample space S, when a die is tossed once .

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363.

Describe the sample space for the following experiment.
A coin is tossed and a die is thrown (rolled).

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364.

Describe the sample space for the following experiment.
A coin is tossed and a die is rolled only in case a head is shown on the coin.

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365. An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

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366. A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

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367. 2 boys and 2 girls are in Room X, and 1 boy and 3 girls are in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

The two rooms are X and Y.
$rightwards double arrow$ The sample space for selection of a room is $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
Let the two boys and two girls in room X be specified as $straight B subscript 1 comma space straight B subscript 2 comma space straight G subscript 1 comma space straight G subscript 2$

$rightwards double arrow$ The sample space for the selection of a person from room X is
$straight S subscript 2 space equals space left curly bracket straight B subscript 1 comma space straight B subscript 2 comma space straight G subscript 1 comma space straight G subscript 2 right curly bracket$
Let one boy and three girls in room Y be specified as $straight B subscript 3 comma space straight G subscript 3 comma space straight G subscript 4 comma space straight G subscript 5.$
$rightwards double arrow$ The sample space for the selection of a person from room Y is
$space space space space straight S subscript 3 space equals space left curly bracket straight B subscript 3 comma space straight G subscript 3 comma space straight G subscript 4 comma space straight G subscript 5 right curly bracket$
If person is selected from room X, we have to combine with sample space $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ and if the person is selected from room Y, we have to combine with sample space $straight S subscript 3.$
Hence, the combined sample space is :
$straight S equals open curly brackets XB subscript 1 comma space XB subscript 2 comma space XG subscript 1 comma space XG subscript 2 comma space YB subscript 3 comma space YG subscript 3 comma space YG subscript 4 comma space YG subscript 5 close curly brackets$

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

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369. An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in the number of girls in the family?

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370.

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

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