Question

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

Answer 1

the probability that both numbers are odd numbers less than 6 if the same numbers cannot be chosen twice. 1/12

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

the probability that both numbers are even numbers if the same numbers cannot be chosen twice 1/6

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

Explanation:

Answer 2

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