The probability that an applicant has at least one of the skills

Q&A
#1

In the Probabilities of Multiple Random Experiments #3, we are told to calculate the probability “The probability that an applicant has at least one of the skills.”

The answer to this question is then as follows:
at_least_one_skill <- 0.2 + 0.3 + 0.4 - (0.2 * 0.3) - (0.2 * 0.4) - (0.3 * 0.4) + (0.2 * 0.3 * 0.4)

I don’t understand this at all, and I also don’t even feel like I was prepared to tackle a question like this. We were taught about the addition and multiplication rule, but I just don’t see the logic of how this answer came to be.

Any help would be appreciative.

#2

@39230239.jakaka could you please include a link?

#3

https://app.dataquest.io/m/407/probabilities-of-multiple-random-experiments/1/multiple-random-experiments

#4

From set theory:

n(AUBUC) = n(A) + n(B) +n(C) - n(AnB) - n(AnC) - n(BnC) + n(AnBnC).

This is similar to this for probability:

P(AUBUC) = P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC).

Therefore,
P(SQL or ML or Viz) = P(SQL) + P(ML) + P(Viz) - P(SQL n ML) - P(SQL n Viz) - P(ML n Viz) + P( SQL n ML n Viz)

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