Mathematics: Thirty percent of the cfa candidates have a degree in economics. a random sample of three cfa candidates is selected. what is the probability that at least one of them has a degree in economics?

Thirty percent of the cfa candidates have a degree

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lb31224

10.01.2022

Mathematics

This is an example of a random variable that follows Bernoulli distribution.

Whenever you perform experiments, with probability of success, the provability of havin successes is

$P(X=k)=\displaystyle\binom{n}{k}p^k(1-p)^{n-k}$

In this case, you have n=3 (you choose a sample of 3 candidates), p=0.3 (30% of candidates have a degree in economics) and we want to be at least one.

One way to solve this is to consider that

$P(X\geq 1)=P(X=1)+P(X=2)+P(X=3)$

But it is much quicker to observe that

$P(X\geq 1)=1-P(X$

And we have

$P(X=0)=\displaystyle\binom{3}{0}0.3^0\cdot 0.7^{3}=1\cdot 1\cdot 0.7^3$

So, the probability that at least one of them has a degree in economics is

1-0.7^3 = 0.657

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Ответ:

leylaanddade

24.07.2021

Mathematics

dynamic and hesitant go in the energetic movements

listless and stumbling go in the sluggish movements

Hope this helped

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Thirty percent of the cfa candidates have a degree in economics. a random sample of three cfa candidates is selected. what is the probability that at least one of them has a degree in economics?

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