If q is chosen from the set {1, 3, 5, 7, 9} and r from {2, 4, 6, 8, 10}, what is the probability that q + r equals 11?

To find the probability that ( q + r = 11 ), we first need to identify the possible values of ( q ) and ( r ) from their respective sets. The set for ( q ) is {1, 3, 5, 7, 9} and for ( r ) is {2, 4, 6, 8, 10}.

Next, we will calculate all the pairs ( (q, r) ) where the sum equals 11. We can list out the combinations:

• If ( q = 1 ), ( r ) would need to be 10 (which is available).

• If ( q = 3 ), ( r ) would need to be 8 (which is available).

• If ( q = 5 ), ( r ) would need to be 6 (which is available).

• If ( q = 7 ), ( r ) would need to be 4 (which is available).

• If ( q = 9 ), ( r ) would need to be 2 (which is available).

From the pairs above, the successful combinations where ( q + r = 11 \