In pea plants, round seeds are dominant and wrinkled seeds are recessive. a pea plant with round seeds was pollinated with a pea plant with wrinkled seeds. the offspring produced round seeds. one of the offspring was mated with a pea plant with heterozygous genes for round seeds.

what are the chances that the offspring will have wrinkled seeds?

1/4.
Assume round gene as A and wrinkled gene as a.
First we can learn that plant with wrinkled seeds must has gene aa because gene a is recessive.
Because the offspring produces all round seeds, the gene of the offspring must be Aa.
The heterogeneous plant, literally, has gene Aa too.
So the seeds after mated should have 3 types: AA, Aa, aa and the ratio will be 1:2:1. the wrinkled seeds have gene aa, so the chance is 1/(1+2+1)=1/4.