[Math] probability of drawing exactly one white marble with replacement

probability

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.

Best Answer

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

agreed?

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.

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