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

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