Need help with question about finding probability

Question

Angel Sanchez has seven books on a shelf: 4 mysteries, 2 science fiction books, and 1 biography.. Two books will be selected at random. With replacement and without replacement determine the probability of selecting at least one science fiction book

Answer 1

(a) With replacement:

 

One way to do it is 1-P(no SF books) = 1 - (5/7)(5/7)

 

Another way is P(SS')+P(S'S)+P(SS) = (2/7)(5/7) + (5/7)(2/7) + (2/7)(2/7)

 

(b) Without replacement can be done similarly.

 

 

Any questions reply back.

Answer 2

With replacement the answer is 2/7 + 2/7.

 

Without replacement the answer is 2/7 + 2/6

 

Without replacement your numerator decreases by one each time you select.