Three bags contain 3 red, 7 black; 8 red, 2 black, and 4 red & 6 black balls respectively. One of the bags is selected at random and a ball is drawn from it. If the ball drawn is red, find the probability that it is drawn from the third bag.

A password of 7 digits is made of digits 9260020.   How long would it take to try all the possible passwords if trying one password takes 5 seconds?

Which of the following events are mutually exclusive?

A bag contains 4 red balls and 6 blue balls. Two balls are drawn at random (without replacement). What is the probability that both balls drawn are of the same color?

A game at a carnival involves rolling a fair six-sided die. The payouts are as follows: If you roll a 6, you win $10. If you roll a 4 or 5, you win $5. If you roll a 1, 2, or 3, you win nothing ($0$). What is the expected payout per roll (i.e. Find the expected value) ?

Find the general antiderivative. Assume

Suppose that and are integrable and that 

The base pair on top is most likely:

Most sequence specific DNA binding proteins interact with DNA in the major grove.  What is the primary reason this is true? 

Histone proteins vary in sequence and function among eukaryotes.