In Super Mario Bros which button is used to run and to jump?

In Super Mario Bros which button is used to run and to jump? I'm asking this question because I heard that most of games use the button A to jump. If my memory is good it is the button B that is used to jump in Super Mario Bross Game. But on the NES gamepad the button A is on the right and the button B on the left, right?

A is used to jump. I most of the game A is used to jump. B is used to run.

On the NES gamepad (and gamecube) the buttons A and B are reversed compared to the Xbox 360, Xbox One, and other conventional gamepad. Then in term of position in most of games you jump with the bottom left button, in Mario Bros you jump with the upper right button.

A is used to jump or swim up, whereas B is used to shoot a flame or run. Have a look at the current world record speedrun to see it in action.

If you're actually asking how one would use both buttons, I can at least tell you how I played it. I placed my thumb on the B and would press A with the joint (similar to the player in the video):

That's actually the way for most of the NES jump 'n runs.

Source: I own a NES and the game ;).