👤
Answered

Obtenez des réponses personnalisées à vos questions sur FRstudy.me. Bénéficiez de conseils étape par étape pour toutes vos questions techniques, grâce aux membres bien informés de notre communauté.

Of a group of 200 persons, 100 are interested in Music, 70 are interested in photography and 40 like skiing. Also 40 are interested in both Music and photography, 30 ni both Music and skiing, 20 ni both photography and skiing, while 20 are interested in photography but not in Music or skiing How many persons are interested in al the three?
A. 40 B. 20 C. 5 D. 8 E. 10

Sagot :

PROTIValkogolya

Réponse:

To find the number of persons interested in all three activities (Music, photography, and skiing), we can use the principle of inclusion-exclusion.

Let:

- A = number of persons interested in Music

- B = number of persons interested in photography

- C = number of persons interested in skiing

- n(A) = 100

- n(B) = 70

- n(C) = 40

- n(A ∩ B) = 40

- n(A ∩ C) = 30

- n(B ∩ C) = 20

- n(B - A - C) = 20

We want to find n(A ∩ B ∩ C).

Using the principle of inclusion-exclusion:

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C) + n(B - A - C)

Plugging in the values:

200 = 100 + 70 + 40 - 40 - 30 - 20 + n(A ∩ B ∩ C) + 20

200 = 220 - 90 + n(A ∩ B ∩ C)

n(A ∩ B ∩ C) = 70

Therefore, there are 10 persons interested in all three activities: Music, photography, and skiing.

Answer: E. 10

Nous sommes ravis de vous avoir parmi nous. Continuez à poser des questions, à répondre et à partager vos idées. Ensemble, nous créons une ressource de savoir précieuse. FRstudy.me est votre source de réponses fiables et précises. Merci pour votre visite et à très bientôt.