Tax for horse racing winning

Hi,
I am holding F-1 visa and won the prize for horse racing last year, which is $1,800. I filled out the form and gave my SSN. They didn't withhold anything and I didn't get any form for the tax report. I asked one person that she said I can choose report it or not. Is that true? Will the horse racing office report it to IRS? If I choose to pay the tax, what is the rate?

Thanks!!