Probability of marbles

Question

10 red marbles and 10 blue marbles are placed into a bag. Alex mixes up the bag and randomly selects a marble. He continues to do so, replacing the marble after each selection, until a red marble is selected.

 

 a. What is the probability that the first time that a red marble is pulled is on Alex’s 6th try?

 

b. On average, how many marbles will Alex have to pull in order to get a red marble? (Hint: use math expectation)

Answer 1

There are 20 marbles total

10 Red

10 Blue

 

Since the marbles are with replacement, it means each pick is independent of the other-- the probability of each pick will be the same.

a.)Probability of picking red marble==> P(Red)= 10/20 (Since the marbles are placed back in bag after each pick, then same probability occurs each pick. So, it doesn't matter which try, 1st, 2nd, 3rd, 4th, 5th or 6th,.. the probability of picking a red marble will still be 10/20 or 0.5.

b.) P(Red)= 10/20=1/2 (On average, for every 2 marbles chosen, 1 will be red. Or, 1 out of 2 picks)