A box contains three white marbles and two black marbles. A marble is drawn at random and replaced in the box three times. Find the probability that exactly one white marble is drawn. Find also the probability that at least one white marble is drawn.


Ok, lets do the first part to begin.

I don't really want to give you the answer straight out.

How much do you understand probability to begin with?

So EXACTLY 1 white means we want the probability for the event

(W,B,B) OR (B,W,B) OR (B,B,W)

since these are the only possible ways that we could draw exactly one white, agreed?

Can you calculate this probability on your own?

Do you understand how to think about "AND" and "OR" in probability terms? If not I can explain further, but you haven't given many details.

Then for the second part, we want AT LEAST 1 white.

That is, we want either

1 white, OR 2 whites, OR 3 whites


So using the method of part a), you should be able to calculate the probability for 2 whites and the probability for 3 whites, and then using the "AND" and/ or "OR" laws for probabilities you should be able to answer this second part of the question.

Does this help?

If you give me some more details of which bit you are getting stuck at I can help you further if you need.

  • $\begingroup$ Excellent that gives me a great starting point from which to attempt the question. I am wondering for the second part concerning at least 1 white I will need to use the probability of event 1 event 2 etc.? $\endgroup$ – user141970 Apr 9 '14 at 21:45
  • $\begingroup$ You're more than welcome. Let me know how you get on. And don't forget to upvote and accept an answer! I'm not sure if I can so shamefully plug myself, but I'm only starting out so I gotta get reputation somewhere! :) Thanks $\endgroup$ – Flint72 Apr 10 '14 at 0:44

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