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 casework

Difficulty rating: 1310

Solution:

A selected number is negative with probability $20/30=2/3$ and positive with probability $10/30=1/3.$ (Selecting exactly $0$ has probability $0.$ ) The product is positive exactly when both numbers have the same sign, so the probability is $\left(\dfrac23\right)^2+\left(\dfrac13\right)^2=\dfrac49+\dfrac19=\dfrac59.$

Thus, the correct answer is D .

2011 AMC 10B Problem 13

Answer: D

Difficulty rating: 1310

Solution:

Problem 13 in Other Years