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Suppose thatb if a person travels the Europe for the first time, the probability that he will visit London is 0.70; Paris is 0.64; Rome is 0.58; Amsterdam is 0.58; London and Paris is 0.45; London and Rome is 0.42; London and Amsterdam is 0.41; Paris and Rome is 0.35; Paris and Amsterdam is 0.39; Rome and Amsterdam is 0.32; London, Paris and Rome is 0.23; London, Paris and Amsterdam is 0.26; London, Rome and Amsterdam is 0.21; Paris, Rome and Amsterdam is 0.20, and all 4 cities is 0.12. What is the probability that he will see at least one of these four cities?

Respuesta :

Answer:

The probability that he will visit at least one of the four cities is 0.88

Step-by-step explanation:

The given information can be presented as follows;

The probability that he will visit London = 0.70 = A

The probability that he will visit Paris = 0.64 = B

The probability that he will visit Rome = 0.58 = C

The probability that he will visit Amsterdam = 0.58 = D

The probability that he will visit;

London and Paris = 0.45 = A∩B

London and Rome = 0.42 = A∩C

London and Amsterdam = 0.41 = A∩D

Paris and Rome = 0.35 = B∩C

Paris and Amsterdam = 0.26 = B∩D

London, Paris and Rome = 0.23 = A∩B∩C

London, Paris, and Amsterdam = 0.26 = A∩B∩D

London, Rome and Amsterdam = 0.21 = A∩C∩D

Paris, Rome and Amsterdam = 0.20 = B∩C∩D

All 4 cities = 0.12 = A∩B∩B∩D

Therefore, the probability, P(at least one), that he will visit at least one of the four cities is the complement of the probability that he will visit all the four cities

∴ P(at least one) = (A∩B∩B∩D)' = 1 - (A∩B∩B∩D) = 1 - 0.12 = 0.88

P(at least one) = 0.88

Which gives, the probability that he will visit at least one of the four cities = 0.88.

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