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Construct sample spaces for single-step experiments with equally likely outcomes (VCMSP266)

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LO: To construct a single-step experiment.

Know:

How to construct an experiment.
How to construct a tally table to collect data from single step experiments.

Understand:

that sample spaces can be constructed for single-step experiments.

Do:

I can construct a sample space for single-step experiments.

[/fusion_text][fullwidth background_color=”” background_image=”” background_parallax=”none” enable_mobile=”no” parallax_speed=”0.3″ background_repeat=”no-repeat” background_position=”left top” video_url=”” video_aspect_ratio=”16:9″ video_webm=”” video_mp4=”” video_ogv=”” video_preview_image=”” overlay_color=”” overlay_opacity=”0.5″ video_mute=”yes” video_loop=”yes” fade=”no” border_size=”0px” border_color=”” border_style=”” padding_top=”20″ padding_bottom=”20″ padding_left=”0″ padding_right=”0″ hundred_percent=”no” equal_height_columns=”no” hide_on_mobile=”no” menu_anchor=”” class=”” id=””][title size=”1″ content_align=”left” style_type=”none” sep_color=”” margin_top=”” margin_bottom=”” class=”” id=””]

Single-Step Experiments

[/title][three_fourth last=”no” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][imageframe lightbox=”no” lightbox_image=”” style_type=”none” hover_type=”none” bordercolor=”” bordersize=”0px” borderradius=”0″ stylecolor=”” align=”center” link=”” linktarget=”_self” animation_type=”0″ animation_direction=”down” animation_speed=”0.1″ hide_on_mobile=”no” class=”” id=””] [/imageframe][imageframe lightbox=”no” lightbox_image=”” style_type=”none” hover_type=”none” bordercolor=”” bordersize=”0px” borderradius=”0″ stylecolor=”” align=”center” link=”” linktarget=”_self” animation_type=”0″ animation_direction=”down” animation_speed=”0.1″ hide_on_mobile=”no” class=”” id=””] [/imageframe][/three_fourth][one_fourth last=”yes” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][fusion_text]

A single-step experiment means a trial using only 1 step.

For example, rolling a die once then recording the result or flipping a coin once is a single-step experiment.

A multi-step experiment means that multiple (more than one) trials are used.

For example, rolling a die then flipping a coin. Or picking the winner and 2nd place finisher in the Melbourne Cup.

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What is a Sample Space?

The sample space of an experiment is a list of all of the possible outcomes for a single-step experiment.

For example, the sample space for the outcome of rolling a die would be 1,2,3,4,5 and 6 and the sample space for the outcome of flipping a coin would be heads or tails.

Equally Likely Outcomes

[/title][one_third last=”no” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][imageframe lightbox=”no” lightbox_image=”” style_type=”none” hover_type=”none” bordercolor=”” bordersize=”0px” borderradius=”0″ stylecolor=”” align=”center” link=”” linktarget=”_self” animation_type=”0″ animation_direction=”down” animation_speed=”0.1″ hide_on_mobile=”no” class=”” id=””] [/imageframe][/one_third][one_third last=”no” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][imageframe lightbox=”no” lightbox_image=”” style_type=”none” hover_type=”none” bordercolor=”” bordersize=”0px” borderradius=”0″ stylecolor=”” align=”center” link=”” linktarget=”_self” animation_type=”0″ animation_direction=”down” animation_speed=”0.1″ hide_on_mobile=”no” class=”” id=””] [/imageframe][/one_third][one_third last=”yes” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][fusion_text]

Equally-likely outcomes are situations that have a 50/50 chance (50%) of happening.

For example, rolling a die and seeing whether it lands as an odd or even number is an equally-likely outcome because there is an equal chance of it landing odd (1,3 or 5) compared to landing even (2, 4, or 6). Flipping a coin and seeing whether it lands heads or tails is also an equally-likely outcome.

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Student Work

[/title][imageframe lightbox=”no” lightbox_image=”” style_type=”none” hover_type=”none” bordercolor=”” bordersize=”0px” borderradius=”0″ stylecolor=”” align=”center” link=”” linktarget=”_self” animation_type=”0″ animation_direction=”down” animation_speed=”0.1″ hide_on_mobile=”no” class=”” id=””] [/imageframe][/fullwidth][fullwidth background_color=”” background_image=”” background_parallax=”none” enable_mobile=”no” parallax_speed=”0.3″ background_repeat=”no-repeat” background_position=”left top” video_url=”” video_aspect_ratio=”16:9″ video_webm=”” video_mp4=”” video_ogv=”” video_preview_image=”” overlay_color=”” overlay_opacity=”0.5″ video_mute=”yes” video_loop=”yes” fade=”no” border_size=”0px” border_color=”” border_style=”” padding_top=”20″ padding_bottom=”20″ padding_left=”0″ padding_right=”0″ hundred_percent=”no” equal_height_columns=”no” hide_on_mobile=”no” menu_anchor=”” class=”” id=””][title size=”1″ content_align=”left” style_type=”none” sep_color=”” margin_top=”” margin_bottom=”” class=”” id=””]

ACARA Work Samples

Chance Experiments Videos

[/title][one_half last=”no” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”https://www.youtube.com/watch?v=RdehfQJ8i_0″ width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”yes” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”aicQnKmmfyM” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”yes” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”https://www.youtube.com/watch?v=LEK1wEzygIM” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][/fullwidth][fullwidth background_color=”” background_image=”” background_parallax=”none” enable_mobile=”no” parallax_speed=”0.3″ background_repeat=”no-repeat” background_position=”left top” video_url=”” video_aspect_ratio=”16:9″ video_webm=”” video_mp4=”” video_ogv=”” video_preview_image=”” overlay_color=”” overlay_opacity=”0.5″ video_mute=”yes” video_loop=”yes” fade=”no” border_size=”0px” border_color=”” border_style=”” padding_top=”20″ padding_bottom=”20″ padding_left=”0″ padding_right=”0″ hundred_percent=”no” equal_height_columns=”no” hide_on_mobile=”no” menu_anchor=”” class=”” id=””][title size=”1″ content_align=”left” style_type=”none” sep_color=”” margin_top=”” margin_bottom=”” class=”” id=””]

FUSE Resources

[/title][imageframe lightbox=”no” lightbox_image=”” style_type=”none” hover_type=”none” bordercolor=”” bordersize=”0px” borderradius=”0″ stylecolor=”” align=”center” link=”https://fuse.education.vic.gov.au/Resource/LandingPage?ObjectId=fbd75d64-75b5-41d7-808b-58ca6de7713a&SearchScope=All” linktarget=”_self” animation_type=”0″ animation_direction=”down” animation_speed=”0.1″ hide_on_mobile=”no” class=”” id=””] [/imageframe][imageframe lightbox=”no” lightbox_image=”” style_type=”none” hover_type=”none” bordercolor=”” bordersize=”0px” borderradius=”0″ stylecolor=”” align=”center” link=”http://fusecontent.education.vic.gov.au/5c95471b-0774-41ae-a48d-cb0740cec45e/p/index.html” linktarget=”_self” animation_type=”0″ animation_direction=”down” animation_speed=”0.1″ hide_on_mobile=”no” class=”” id=””] [/imageframe][/fullwidth][imageframe lightbox=”no” lightbox_image=”” style_type=”none” hover_type=”none” bordercolor=”” bordersize=”0px” borderradius=”0″ stylecolor=”” align=”none” link=”http://www.alamandamaths.com/statistics-and-probability/chance/complementary-events-and-sum-of-probabilities/” linktarget=”_self” animation_type=”0″ animation_direction=”down” animation_speed=”0.1″ hide_on_mobile=”no” class=”” id=””] [/imageframe]