huda wrote:
R and S are independent events. The probability of event R occurring is greater than the probability of event S occurring.
Quantity A |
Quantity B |
Probability of R and S occurring |
Probability of R or S occurring |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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) =
rsWe also know that: P(R OR S) = P(R) + P(S) - P(R AND S) =
r + s - rsWe now have:
QUANTITY A:
rsQUANTITY B:
r + s - rsAdd 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