In all cases, the events are independent. That's why we have to multiply the results.
Probability that both numbers are greater than 6 if the same number can be chosen twice.
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P = 3 / 9 * 3 / 9 = 1/9 because possible outcomes are the pairs (7,8), (7,9) and (8,9).
Probability that both numbers are less than 7 if the same number can be chosen twice
P = 6 / 9 * 6 / 9 = 4/9
Probability when both numbers are odd numbers less than 6 if the same numbers cannot be chosen twice
P = 3/9 * 2/8 = 1/12, odd numbers less than 6 are 1, 3 and 5. If the same number cannot be chosen depending on these numbers, we'll end up with 2 in possible outcome for the 2nd pair of the probability.
Probability that both numbers are even numbers if the same numbers cannot be chosen twice is
P = 4/9 * 3/9 = 4/27. The same logic is possible in this case, as well
Answer:
the probability that both numbers
are greater than 6 if the same
number can be chosen twice =1/9
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 odd numbers less than 6 if the
same numbers cannot be chosen
twice =1/12
the probability that both numbers
are even numbers if the same
numbers cannot be chosen twice =1/6
