球 and 球技: a ball or sphere and a category of sports
Compare a thrown ball and a dirt sphere with preferences and possible participation in ball sports.
球: a pitched ball and a dirt sphere
球 (たま) means ball or sphere. 「投手が速い球を低めに投げた。」 means “The pitcher threw a fast ball low.” The pitcher threw a fast ball low; 球 names the object.
「子どもが土を丸めて小さな球を作った。」 means “The child rolled the dirt into a small sphere.” The child made a small sphere from dirt, without naming sports equipment.
球技: preferences and sports available to try
球技 (きゅうぎ) means ball sport. 「弟は走る競技より球技が好きだ。」 means “My younger brother prefers ball sports to running events.” Ball sports are the category the younger brother prefers to running events.
「体育館では三種類の球技を体験できる。」 means “You can try three kinds of ball sports in the gymnasium.” 体験できる expresses the possibility of trying three kinds.
Separate objects, categories, and possibilities
球 refers to objects in these examples, while 球技 names a category of activities.
The gymnasium sentence does not name the three sports or report completed participation.
Does 体験できる establish that all three 球技 have been tried and identify their names?
Show the answer and why
No. It states that three kinds can be tried. Neither completed participation nor the three names is supplied.