Meaning:

Depend totally on one single person or course of action.

If you put all your eggs into one basket, you put all your energy and time to one thing or purpose. If it fails, you will have no other possibilities left.

Example:

I know you really want to go to BYU, but don't put all your eggs into one basket. Apply to a few other colleges too.

I'll invest my money in several companies, not this one only. I don't want to put all my eggs into one basket.

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