Question

Sara selects two of the seven colors of the rainbow, one after another, with replacement. What is the probability that the first color is red and the second is orange?

Answer 1

Well, there are actually millions of colors in the rainbow, (every color that the human eye can see), but I do understand the question you're asking:

 

-- When Sara is ready to make her first selection, there are seven things with different colors in the pot, and one of them is red.

The probability that she picks the red one is ( 1 / 7 ).

The question says "with replacement". That means that after she selects it and looks at it, she puts it back in the pot. So . . .

-- When she's ready to make her second selection, the same seven things with different colors are still in the pot.  One of them is orange.

The probability that she picks the orange one is ( 1 / 7 ).

-- The probability of BOTH selections being successful (the color she wants) is

(1/7) x (1/7) .

That's (1/49), which is about  2.04 percent .