omg i feel stupid for asking this question cause I cant get it, im probs tired or something, but here it is anyways:

One layer of tinting material on a window cuts out 1/5 of the sun's UV rays.

1)what fraction would be cut out by using two layers?

2) How many layers would be required to cut out at least 9/10 of the sun's UV rays?

Answers:

1)9/25

2)11

SHOWS me workings!! fanks

This is a series type question, not probability.

Let x be the amount of the sun's rays that hits the material

First layer takes out x/5 so after the first layer there is only 4x/5 left that is not cut

When it hits the second layer, only 4x/5 of rays pass through and a fifth of that is removed

i.e. (4x/5)(1/5) is removed

Total amount cut = x/5 + 4x/25 = 9x/25 so fraction of rays cut is 9/25

Note that after each layer we multiply the amount of rays that entered by 4/5 since 1/5 is removed.

In terms of proportions:

After 1st layer the fraction of rays left is (4/5)

After 2nd layer the fraction of rays left is (4/5)

^{2}
After 3rd layer the fraction of rays left is (4/5)

^{3}
...

After nth layer the fraction of rays left is (4/5)

^{n}
We want the fraction of rays left after the nth layer to be at least 1/10 (as 9/10 is cut out) so

(4/5)

^{n} > 9/10

Using logarithms or otherwise this should yield n = 11 as the lowest integer which satisfies this inequality