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Two numbers are randomly selected on a number line numbered from 1 to 9. Match each scenario to its probability. Tiles the probability that both numbers are greater than 6 if the same number can be chosen twice the probability that both numbers are less than 7 if the same number can be chosen twice the probability that both numbers are odd numbers less than 6 if the same numbers cannot be chosen twice the probability that both numbers are even numbers if the same numbers cannot be chosen twice

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BlueSky06
Numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9

probability that both numbers are greater than 6 if the same number can be chosen twice. 
3² / 9² = 9/81 or 1/9

the probability that both numbers are less than 7 if the same number can be chosen twice
6² / 9² = 36/81 or 4/9

the probability that both numbers are odd numbers less than 6 if the same numbers cannot be chosen twice
3/9 * 2/8 = 6/72 or 1/12

the probability that both numbers are even numbers if the same numbers cannot be chosen twice
4/9 * 3/9 = 12/81 or 4/27
MrRoyal

The sample size is given as:

  • n = 9 i.e. numbers 1 to 9

So, the sample space is:

  • S = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Selection of numbers greater than 6, twice

There are 3 numbers greater than 6.

So, the probability of selecting a number greater than 6 is:

[tex]P(6) = \frac 39[/tex]

[tex]P(6) = \frac 13[/tex]

When the numbers are selected twice, the probability is:

[tex]p = (\frac 13)^2[/tex]

[tex]p = \frac 19[/tex]

So, the probability that both numbers are greater than 6 if the same number can be chosen twice is 1/9

Selection of numbers less than 7, twice

There are 6 numbers less than 7.

So, the probability of selecting a number less than 7 is:

[tex]P(7) = \frac 69[/tex]

[tex]P(7) = \frac 23[/tex]

When the numbers are selected twice, the probability is:

[tex]p = (\frac 23)^2[/tex]

[tex]p = \frac 49[/tex]

So, the probability that both numbers are less than 7 if the same number can be chosen twice is 4/9

Selecting odd numbers less than 6

There are 3 odd numbers less than 6.

So, the probability of selecting an odd number less than 6 is:

[tex]P(odd) = \frac 39[/tex]

When the numbers are selected twice (without replacement), the probability is:

[tex]p = \frac 39 \times \frac 28[/tex]

This gives

[tex]p = \frac 13 \times \frac 14[/tex]

[tex]p = \frac 1{12}[/tex]

So, the probability that both numbers are odd numbers less than 6 is 1/12

Selecting even numbers

There are 4 even numbers

So, the probability of selecting an even number is:

[tex]P(even) = \frac 49[/tex]

When the numbers are selected twice (without replacement), the probability is:

[tex]p = \frac 49 \times \frac 39[/tex]

This gives

[tex]p = \frac 49 \times \frac 13[/tex]

[tex]p = \frac 4{27}[/tex]

So, the probability that both numbers are even numbers is 4/27

Read more about probabilities at:

https://brainly.com/question/4079902

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