Adding many random reals may add many Cohen reals

Abstract

Let $\kappa$ be an infinite cardinal. Then, forcing with $\mathbb{R}(\kappa )$$\times$$\mathbb{R}(\kappa )$ adds a generic filter for $\mathbb{C}(\kappa );$ where $\mathbb{R}(\kappa )$ and $\mathbb{C}(\kappa )$ are the forcing notions for adding $\kappa$-many random reals and adding $\kappa$-many Cohen reals respectively.