Probability of scoring at basketball given probability of not scoring

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Christian Lawson-Perfect

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Christian Lawson-Perfect 7 years, 7 months ago

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Created this as a copy of The probability of an event not happening - five friends play mini golf.

Name	Status	Author	Last Modified
The probability of an event not happening - five friends play mini golf	Ready to use	Elliott Fletcher	19/12/2022 12:28
Probability of scoring at basketball given probability of not scoring	Ready to use	Christian Lawson-Perfect	20/11/2019 14:41
Hugh's copy of The probability of an event not happening - five friends play mini golf	draft	Hugh O'Donnell	16/01/2018 13:48
Simon's copy of The probability of an event not happening - five friends play mini golf	draft	Simon Thomas	08/05/2019 09:46
Maria's copy of Probability of scoring at basketball given probability of not scoring	draft	Maria Aneiros	27/05/2019 02:29
The probability of an event not happening - five friends play mini golf	draft	Xiaodan Leng	11/07/2019 02:02
Probability of scoring at basketball given probability of not scoring	draft	Xiaodan Leng	11/07/2019 02:03

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Question statement

You are playing a game of basketball against your friend. You have the ball but your friend is blocking you from moving forwards so you throw the ball and hope that it goes through the hoop.

The probability that the ball misses the hoop is $\displaystyle \frac{1}{\var{Hoop}}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

Hoop

integer

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(5..9)

JME function reference

Description

Denominator of the fraction for the probability that the ball misses the hoop.

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Advice

All probability situations can be reduced to two possible outcomes: success or failure.

When we express the outcomes in this way we say that they are complementary.

The sum of the probability of an event and its complement is always $1$ .

If $\mathrm{P}(\mathrm{E})$ is the probability of an event $\mathrm{E}$ happening and $\mathrm{P}(\bar{\mathrm{E}})$ is the probability of that event not happening then

$\mathrm{P}(\mathrm{E}) +\mathrm{P}(\bar{\mathrm{E}}) = 1.$

Rearranging this equation gives:

$\mathrm{P}(\bar{\mathrm{E}}) = 1 - \mathrm{P}(\mathrm{E})$

When we throw the ball we can say that there are two possible outcomes: either the ball goes through the hoop or the ball does not go through the hoop (the ball misses the hoop).

Let $\mathrm{H}$ be the event that the ball goes through the hoop. Then

$\mathrm{P}(\mathrm{H}) + \mathrm{P}(\bar{\mathrm{H}}) = 1.$

But we are given that $\mathrm{P}(\bar{\mathrm{H}}) = \displaystyle\frac{1}{\var{Hoop}}$ .

Rearranging the above equation to obtain $\mathrm{P}(\mathrm{H})$ .

$\begin{align} \mathrm{P}(\mathrm{H}) &= 1 - \mathrm{P}(\bar{\mathrm{H}}) \\[0.5em] &= 1 - \displaystyle\frac{1}{\var{Hoop}}\\[0.5em] &= \simplify[fractionNumbers]{{1-1/{Hoop}}}. \end{align}$

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Probability of scoring at basketball given probability of not scoring

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Taxonomy: mathcentre

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Taxonomy: Context

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Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Error in variable testing condition

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Generated value: `integer`

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Number entry

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Probability of scoring at basketball given probability of not scoring

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`