Leoni is participating in four drawing competitions. If the probability of her losing any drawing competition is 0.7, find the probability of her winning
a) at least one competition.
b) exactly two competitions.

(a)

(b)

Explanation:

Represent losing with L and winning with W.

So:

--- Given

Probability of winning would be:

The question illustrates binomial probability and will be solved using the following binomial expansion;

So:

Solving (a): Winning at least 1

We look at the above and we list out the terms where the powers of W is at least 1; i.e., 1,2,3 and 4

So, we have:

Substitute value for W and L

Hence, the probability of her winning at least one is 0.7599

Solving (a): Wining exactly 2

We look at the above and we list out the terms where the powers of W is exactly 2

So, we have:

Substitute value for W and L

Hence, the probability of her winning exactly two is 0.2646

Given that the Washington State has a serious problem of lack of water, while Iowa has the opposite problem, a balance should be sought to redistribute this proportion of water between the states.

The most viable and appropriate option to resolve this situation would be to build a dam on the Mississippi River, which forms the eastern border of the state and collects the largest amounts of rainwater in its flow.

Then, this dam should be connected through channels and aqueducts with the other Iowa rivers, such as the Cedar River, until reaching the Missouri River, the river that marks the eastern border of the state.

There, the course of the aqueducts should be piped so that they run underground to the west, supplying not only the Washington State, but all the states that in the course of the pipeline have aridity problems, through different extraction and pumping points.