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Let 
denote the event that a student is a freshman, 
a sophomore, 
a junior, and 
a senior.
Let
denote the event that a student majors in engineering. By the law of total probability,
By the definition of conditional probability, we can expand each of these intersection probabilities to get
Let
By the definition of conditional probability, we can expand each of these intersection probabilities to get
It would take Sarah 0.15 years more than Brandon to get $1,530 in her account.
Step-by-step explanation:
Step 1; First, we need to calculate the interest per year for both Brandon and Sarah.
For Brandon, if 3 % is compounded monthly, then yearly interest = 3.75 × 12 = 45% is compounded yearly. So 0.45 × $510 = $229.50 is compounded annually.
For Sarah, if 3 % is compounded monthly, then yearly interest = 3.625 × 12 = 43.5% yearly. So 0.435 × $510 = $221.85 is compounded annually.
Step 2; If money is three times $510, there would have to be a balance of 3 × $510 = $1,530. As they have already invested $510.
The money needed by interest = $1,530 - $510 = $1,020.
Step 3;
As Brandon gets $229.50 every year, years taken to get $1,020 = = 4.4444 years.
As Sarah gets $221.85 every year, years taken to get $1,020 = = 4.5977 years.
The difference in years = 4.5977 - 4.4444 = 0.1533 years. Rounding this off to the nearest hundredth, we get 0.15 years.