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

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.

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

b) Now we want both tiles to be white.

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

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

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

Probability =

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

the answer is 99.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.