Curable composition and cured product

A curable composition comprising:

• a modifier (A);
• a modified polyphenylene ether (B);
• and
• a radically polymerizable compound (C),
• wherein:
• the modifier (A) comprises a modified resin (A1) and core-shell polymer particles (A2),
• the modified resin (A1) comprises a modified styrene-based elastomer (A1-1),
• the modified resin (A1) and the core-shell polymer particles (A2) are modified with a monomer having one or more polar groups selected from the group consisting of an epoxy group, an amino group, an acid anhydride group, a hydroxy group, and a carboxy group,
• a type of a group with a largest amount among the one or more polar groups of the modified resin (A1) is the same as a type of a group with a largest amount among the one or more polar groups of the core-shell polymer particles (A2),
• the modified polyphenylene ether (B) comprises a carbon-carbon unsaturated double bond-containing group bonded to an oxygen atom at a molecular chain terminal, and
• the radically polymerizable compound (C) comprises two or more radically polymerizable carbon-carbon unsaturated double bonds.