Let P(even R occurring) = r
Let P(even S occurring) = s
GIVEN: r > s

Since R and S are independent events, we know that P(R AND S) = rs
We also know that: P(R OR S) = P(R) + P(S) - P(R AND S) = r + s - rs

We now have:
QUANTITY A: rs
QUANTITY B: r + s - rs

Add rs to both quantities to get:
QUANTITY A: 2rs
QUANTITY B: r + s

Divide both quantities by s to get:
QUANTITY A: \(2r\)

QUANTITY B: \(\frac{r + s}{s}\)

A useful fraction property says: \(\frac{a + b}{c }=\frac{ a}{c} + \frac{b}{c}\)

When we apply the above property to Quantity B we get:

QUANTITY A: \(2r\)

QUANTITY B: \(\frac{r}{s}+\frac{s}{s}\)

Simplify to get:
QUANTITY A: \(2r\)

QUANTITY B: \(\frac{r}{s}+1\)

Since we're told that r > s, we know that \(\frac{r}{s}\) is greater than 1, which means \(\frac{r}{s}+1 > 2\)

So, we get:
QUANTITY A: \(2r\)
QUANTITY B: Some number greater than 2

Since the maximum possible value of r is 1, the greatest possible value of Quantity A is 2.
So we can see that Quantity B will always be greater than Quantity A

Answer: B

Cheers,
Brent