Maths help

A bag contains 3 green and 5 blue marbles. If Lily picks the marbles and replace them, what is the expected number of times she picks a marble until she gets a blue marble for the second time?

May I have a tip how to start the question? like what kind of equation/distribution am I using there?
Original post by Bookworm524
A bag contains 3 green and 5 blue marbles. If Lily picks the marbles and replace them, what is the expected number of times she picks a marble until she gets a blue marble for the second time?

May I have a tip how to start the question? like what kind of equation/distribution am I using there?

This is the second question you have posted tonight ... you need to post what you've tried as per forum rules.
Original post by Bookworm524
A bag contains 3 green and 5 blue marbles. If Lily picks the marbles and replace them, what is the expected number of times she picks a marble until she gets a blue marble for the second time?

May I have a tip how to start the question? like what kind of equation/distribution am I using there?

Its similar to a geometrical distribution as you keep going until you have a "success". Youre asked for the expected value which is the usual sum over x_i * p_i. So if you keep going until youve picked two blue marbles in each case, what are the p_i's? Drawing it as a "ragged" tree may help you think about the different possiblities.
(edited 4 months ago)
Rather than solve directly for getting 2 blue marbles, you may want to solve for getting one blue marble and then use E[X1+X2]=E[X1]+E[X2].

This is also a very simple case of a negative binomial distribution so it may be helpful to look that up.