please solve p$-$value and correct doctor

A vaccination clinic has two types of vaccines against a disease. Each person who comes in to be vaccinated gets either Vaccine $1$ or Vaccine $2.$ One week, everyone who came in on Monday, Wednesday, and Friday was given Vaccine $1.$ Everyone who came in on Tuesday and Thursday was given Vaccine $2.$ The clinic is closed on weekends.

Doctor DeNero at the clinic said, $"$Oh wow, it's just like tossing a coin that lands heads with chance $$\backslash$frac$\{3\}\{5\}$$$.$ Heads you get Vaccine $1$ and Tails you get Vaccine $2."$

But Doctor Sahai said, $"$No$,$ it's not. We're not doing anything like tossing a coin."

That week, the clinic gave Vaccine $1$ to $211$ people and Vaccine $2$ to $107$ people. Conduct a test of hypotheses to see which doctor's position is better supported by the data.