Question

A bag contains n white tiles and five black tiles. The tiles are all equal in shape and sizes. A tile is drawn at random and is replaced. A second tile is then drawn.
Find
a) the probability that the first tile is white
b) the probability that both the first and second tiles are white

Answer 1

We know that our bag has n white tiles and 5 black tiles.

So, the total number of tiles in the bag is n + 5.

We know that a tile is drawn at random and is replaced, then a second tile is drawn.

a) We want to find the probability that the first tile is white.

Because all the tiles have the same probability of being randomly drawn, the probability of drawing a white tile is just the quotient between the number of white tiles and the total number of tiles in the bag.

$P = n/(n + 5)$

And for the second draw, we do not have any restrictions, so the probability is the above one.

$P = n/(n + 5)$

b) Now we want both tiles to be white.

For the first one we already know the probability, which is:

$P = n/(n + 5)$

And because the tile is replaced, the probability of drawing a white tile again is exactly the same:

$Q =n/(n + 5)$

The joint probability (the probability of both of these outcomes to happen together) is the product of the individual probabilities.

Probability = $P*Q = (n/(n + 5))^2$

If you want to read more about probability, you can read:

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