Question

Two real numbers are selected independently at random from the interval $[-20, 10].$ What is the probability that the product of those numbers is greater than zero?

$\dfrac{1}{9}$

$\dfrac{1}{3}$

$\dfrac{4}{9}$

$\dfrac{5}{9}$

$\dfrac{2}{3}$

Answer: D

Concepts:geometric probability independent events

Difficulty rating: 1390

Solution:

The interval has length $30,$ with $20$ of it negative and $10$ of it positive. So each number is positive with probability $\dfrac13$ and negative with probability $\dfrac23.$

The product is positive when both are positive or both are negative: $\left(\dfrac13\right)^2+\left(\dfrac23\right)^2=\dfrac19+\dfrac49=\dfrac59.$

Thus, the correct answer is D.

2011 AMC 12B Problem 9

Answer: D

Difficulty rating: 1390

Solution:

Problem 9 in Other Years