Two numbers are randomly selected on a number line numbered from 1 to 9. match each scenario to its probability.
tiles
a)the probability that both numbers
are greater than 6 if the same
number can be chosen twice
b) the probability that both numbers
are less than 7 if the same
number can be chosen twice
c)the probability that both numbers
are odd numbers less than 6 if the
same numbers cannot be chosen
twice
d) the probability that both numbers
are even numbers if the same
numbers cannot be chosen twice
pairs
which pair up with options:
1/12
1/9
4/9
1/6

A)the probability that both numbers
are greater than 6 if the same
number can be chosen twice

The combinations in which both numbers are greater than 6 are:

first number        second number
7                          7
7                          8
7                          9
8                          7
8                          8
8                          9
9                          7
9                          8
9                          9

Those are 3 * 3 different combinations = 9 outcomes.

The total number of possible outcomes are 9*9 = 81

So, the probability is 9 / 81 = 1 /9

B) the probability that both numbers
are less than 7 if the same
number can be chosen twice

The combinations in which both numbers are less than 7 are:

First number 1, 2, 3, 4, 5 and 6: 6 outcomes
Second number: 1, 2, 3, 4, 5 and 6: 6 outcomes

Number of combinations in which both numbers are less than 7: 6 * 6 = 36.

Total number of possible combinations of outcomes : 81

Probability = 36 / 81 = 4 / 9

C)the probability that both numbers
are odd numbers less than 6 if the
same numbers cannot be chosen
twice

The odd numbers less than 6 are 1, 3 and 5

First roll          second roll
1                    3
1                    5
3                    1
3                    5
5                    1
5                    3

So they are 6 possible combinations of odd number less than 6, given that the same number cannot be chosen twice.

In this case the total number of outcomes is not 9 * 9 but 9 * 8 = 72 (becasue the second time there are only 8 possible numbers)

The probability is 6 / 72 = 1 / 12

D) the probability that both numbers
are even numbers if the same
numbers cannot be chosen twice

The even numbers the first time are 2, 4, 6 and 8 = 4 different numbers.

The second time you have one less even number = 3.

The number of combinations are 4 * 3 = 12

And the probability is 12 / 72 = 1 / 6

Pairing questions with answers:

A -> 1/9

B -> 4/9

C-> 1/12

D-> 1/6

I’m not sure how this works