Probability

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Games

Posted by mathtnotes at 12:58 PM on April 09, 2009

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Here got some interesting games about the probability, hope you all are enjoy with the games.

Have fun!

PROBABILITY GAME 1

WELCOME TO THE PROBABILITY FAIR

CLICK ME TO START THE GAME

There are few levels of different games in the probability fair:

1) SHELL GAME 2) PLINKO GAME

3)CHIP GAME 4)TICKET WHEEL

PROBABILITY GAME 2

CLICK ON ME TO START THE GAME

Probability of an Event and Expected Number of Times an Event Occurs

Posted by mathtnotes at 10:56 AM on April 09, 2009

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In the previous lesson we learnt about the ratio of an event occurence to the trials is almost a constant when the number of trials is big enough. this ratio of frequency of an event to the total number of trials from a big number of trials like 100, 500 and 1000 times is known as the probability of an event.

From the formula above, we can find the expected number of times an event occurs if the probability and the number of trials are known.

Number of times for event A occurs = P(A) x number of trials.

Please note that the number of an event A occurs is always less than or equal to the number of trials. Therefore,.

If event A never occur then P(A) =0

If event A occur for every trials then P(A)=1

Example 3:

Answer

Enrichment Activity:

www.mathsonline.co.uk/nonmembers/resource/prob/xmas.html

Ratio of Event Occurrence to Trials

Posted by mathtnotes at 09:27 AM on April 09, 2009

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The ratio of the number of times an event occurs to the trials in an experiment may be obtained by collecting appropriate data.

Example:
In a tossing coin experiment, a coin was tossed 10 times. The result is {H,T,H ,T,T,T,H,T,H,T}

Activity:
Please follow the links for the activity.
Instruction:
1. In each activity, please use the number of trials = 20, 50, 100, 500 and 1000
2. For each number of trials, please write down the number of each event that you would expect and from the experiment then calculate the ratio of each event.
3. After getting the result from the experiment, please compare your expected and experimential result.
4. What you can say on the ratio of each event when the number of trials increases?

Links

Event for a sample space

Posted by mathtnotes at 01:13 PM on April 08, 2009

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An event A is a possible event for a sample space S if A is a subset of S and A is not an empty set. If A is an empty set , then A is an event that cannot occur, that is, A is an impossible event.

For example, if the sample space for rolling a dice is S = {1, 2, 3, 4, 5, 6}.

If event A is obtaining an even number,

A = {2, 4, 6},

then A is a possible event.

If event B is obtaining a number greater than 6,

B = { } or

then B is an impossible event.

EXAMPLE 2

Here is a signboard.

A letter or number is selected at random from the signboard.

Sample space, S = {2, 4, H, O, U, R, S, A, T, M}

L = event of selecting a vowel.

L = {A, O, U}

Hence, event L is possible.

Q = event of selecting a number less than 2.

Q =

Hence, Q is impossible.

EXERCISE:

The following toys are on display at the gift section of a department store. A toy is selected at random. Determine whether the following events are possible or impossible.

(a) A jeep is selected.

(b) A blue sports car is selected.

(d) A red car is selected.

Answer

Elements that satisfy a given condition

Posted by mathtnotes at 12:07 PM on April 08, 2009

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From a sample space of an experiment, elements that satisfy a given condition may be listed.

EXAMPLE 1

A dice is rolled.

(a) Write the sample space for the experiment.

S ={1,2,3,4,5,6}

(b) State all elements in the sample space which satisfy the following conditions:

(i) An odd number is obtained.
1,3,5
(ii) A prime number is obtained.
2,3,5

EXAMPLE 2

A spinner is spun.

(a) Write the sample space for the experiment.

S = {L, U, Z, O, E, I}

(b) State the elements in the sample space that satisfy the following conditions:

The pointer points at
(i) a vowel.
E, O,I
(ii) a letter after 'M' in the alphabet.
O, U, Z

CHALLENGE

There are many socks in a drawer but they belong to either one of two colours only. The room is dark and Samad cannot see the colour of the socks. What is the minimum number of socks that he should take to ensure that he gets 2 socks of the same colour?

Table and tree diagram

Posted by mathtnotes at 05:10 AM on April 07, 2009

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Example

Bag A has a yellow card and a pink card. Bag B has the number cards 2, 7, and 9. A card is taken from each bag. List all the possible outcomes and write the sample space.

For an experiment involving 2 trials (as in this case), or 2 set of outcomes, a table is used to list all possible outcomes.

Let Y = yellow and P = pink. Table of all possible outcomes:

Sample space S = { (2, Y), (2, P), (7, Y), (7, P), (9, Y), (9, P)}

Tree diagram

A tree diagram may also be used to list all possible outcomes. For the example above, the tree diagram is given below.

TIP: A tree diagram is useful when an experiment involves more than 2 trials or 2 sets of outcomes.

Sample spaces

Posted by mathtnotes at 08:22 AM on April 06, 2009

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Do you know what is a sample space?

Picture of dice that shown in different outcomes

A sample space can be written by using set notation.

Example 1:

When a dice is rolled, how many outcomes will we get?

There will have 6 possible outcomes shown as above.

The sample space of rolling a dice is

REMEMBER!

Sometimes the outcomes are written in the form of ordered pairs.

EXAMPLE 2:

When we rolled two coins simultaneously, what are the possible outcomes ?

The possible outcomes will  be:

Thus, the sample space S will be

EXERCISE:

BOARD?

In this picture, try to identify the words and find the sample space of each word.

CHALLENGE

RED?YELLOW OR GREEN?

If you pass through three traffic lights on the way to school, what are the chances that you will get stuck with all
red lights? Or all yellow?