# Are these preferences consistent with the independence over lotteries axiom?

Just wondering if these preferences are consistent with the von Neumann Morgenstern independence axiom. I think they are but I am having trouble knowing for sure. thank you!

Lottery a: \$1 with probability 0.99 and \$0 with probability 0.01 Lottery b: \$1 with probability 0.9, \$5 with probability 0.05, and \$0 with probability 0.05 Player prefers lottery b to lottery a Lottery c: \$1 with probability 0.9 and \$0 with probability 0.1 Lottery d: \$0 with probability 0.5 and \$5 with probability 0.5 Player prefers lottery c to lottery d New contributor 12021 is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct. • The dollar sign $ is used to delimit MathJax zones. So when you want to use a dollar sign in your post, you should type \$ (with a backward slash in front). – Herr K. Feb 11 at 22:07 • This looks like a homework question. Instead of asking directly for an answer, you should show what you've tried and where exactly you're stuck. For instance, why do you think the preferences are consistent with independence? How do they conform to the definition of independence? – Herr K. Feb 11 at 22:12 • @HerrK. They are just wondering! Why do you have to assume it is a homework question? Do you not wonder about these things with very specific parameters? I myself often wonder what$\int_{-\infty}^{\infty} e^{-x^2} dx$equals, especially by next Thursday, thank you! – denesp Feb 11 at 22:16 • @denesp: Was just trying to be nice to a new user :) although I have to admit that such moments are becoming rarer and rarer. – Herr K. Feb 11 at 22:25 • And, since I can't wait till next Thursday,$\int_{-\infty}^{\infty}e^{-x^2}dx=\sqrt{\pi}\$ :) – Herr K. Feb 11 at 22:26