The letters that form the word ALGEBRA are placed in a bowl. What is the probability, as a percent, of choosing a letter other than "A" and then choosing an "A&qu…

Question

The letters that form the word ALGEBRA are placed in a bowl. What is the probability, as a percent, of choosing a letter other than "A" and then choosing an "A"?

Answer 1

Explanation:

There are 7 letters in algebra. Two of them are "A"

The probability of choosing "A" on the first try is
`(2)/(7)`

Assuming you remove the letter after choosing it:

If you remove the A, then the second time around you have 6 letters with one of them being A

So, your chances of picking A is
`(1)/(6)`

Multiply the probabilities together.

`(2)/(7) *(1)/(6) =(2)/(42) =(1)/(21)`

Assuming you don't remove the letter after choosing it:

You have the same probability again,
`(2)/(7)`

Square the probability:

`((2)/(7))^2 =(4)/(49)`