Question

wo numbers are randomly selected on a number line numbered from 1 to 9. Match each scenario to its probability. 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 arrowRight arrowRight arrowRight arrowRight

Answer 1

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

Answer 2

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.

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