In a random sample of $10{,}000$ college students, a research company found that $35.7\%$ were involved in a club and $27.8\%$ studied four or more hours per day. When they reported their findings, the research company indicated that $53.4\%$ of college students either were involved in a club or studied four or more hours per day. Given this information, what is the probability that a college student is involved in a club and studies four or more hours per day?