Depends on what was backed up and restored after performing the reinstall. If the malicious file responsible for the ransomware was backeup up...it could start the whole process again.
The safest practice is not to backup
any executable files (*.exe), screensavers (*.scr), (*.pdf), dynamic link library (*.dll), autorun (*.ini) or script files (.php, .asp, .htm, .html, .xml) files because they may be infected by malware. Avoid backing up compressed files (.zip, .cab, .rar) that have executables inside them as some types of malware can penetrate compressed files and infect the .exe files within them. Other types of malware may even disguise itself by hiding a file extension
or by adding double file extensions and/or space(s) in the file's name to hide the real extension as shown here
(click Figure 1 to enlarge
) so be sure you look closely at the full file name. If you cannot see the file extension, you may need to reconfigure Windows to show file name extensions