Question

Topic : Sample Space Diagrams.
Grade : 8

Q U E S T I O N :-

One fair spinner has three sections marked with the numbers 1, 2 and 3.
Another pair spinner have five sections marked with the numbers 1, 2, 3, 4 and 5.

a) Draw a sample space diagram to show all the possible outcomes.

b) Work out the probability of scoring:

i) two 2s
ii) two odd numbers
iii) a total of 5

Answer 1

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A N S W E R :-

→ In attachment !

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E X P L A N A T I O N :-

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a) Draw a sample space diagram to show all the possible outcomes.

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➝ In the attachment.

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b)

i) Two 2s

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➝ Look at the line x, at the top we have 3 then look down you see 2 and according to the two 2s . Then look straight from 2 , we can see the first + now look down we can see 1 but according to the question we have to find two 2s. Again look at 2 on the line x , we can see the second +, now look down we can see 2 so circle the second + . Now you got your answer.

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ii) 2 odd numbers

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➝ In the diagram we can see that it contains 15 +,

We have to find 2 odd numbers. First we have to find the total number of odd numbers. Look at the link x, 3 and 1 are the odd numbers, and from line y , 1, 3 and 5 are the odd numbers.

Look at the top number on line x , look at 3 ( line x ) look at the first + then look down, we get 2 then look down we get the number 1 ( line y ) so circle the first + of number 3 ( line x ). Then, look at the second + , look down, we get the number 2 which is not an odd number. Look at the third + , now look down, we get the number 3 ( odd number ) so circle that + . Now look at the fourth + , then look down, we get the number 4 ( odd number ). Look at the fifth + , look down we get the number 5 ( odd number ). Do the same for the number 1 ( odd number ) on the line x.

After finding all the odd numbers we get a fraction 6/15, if you cancel it then we get 2/5 . Therefore, the answer is 2/5.

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iii) A total of 5

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➝ Here also we are gonna perform the same process which we did for (ii). Look at the number 3 on line x , then look at the first + and look down we get 1 , and 3+1 = 4 not 5, look at the second +, then look down we get the number 2 . We get add 3 with 2 we get 5 .Now look at the number 2 on line x , then look at every + then look down and add the number with 2. If we look at the third +, we get the number 3. And 2+3 = 5. Do the same for the number 1 on the line x . When we look at the number 1 on the line x and look straight to the fourth +, then look down we get the number 4 . And 1+4 = 5.

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Finally you got your answer ;) !