Question

For a group of 200 persons, 100 are interested in music, 70 in photography and 40 in swimming; furthermore 40 are interested in both, music and photography, 30 in both music and swimming, 20 in photography and swimming and 10 in all the three. How many are interested in photography but not in music and swimming?

Answer 1

There are 20 persons who are interested in photography but not in music and swimming.

Step-by-step explanation:

Let

1. Let P(Ph) is number of person interested in photography .
2. Let P(s) is number of person interested in swimming.
3. Let P(m) is number of person interested in music.

Given:

P(ph)=70 , P(s)=40,P(m)=100

$\Rightarrow P\left ( ph\cap s \right )$ =20

$\Rightarrow P\left ( ph\cap m \right )$ = 40

$\Rightarrow P\left ( ph\cap s \cap m \right )$ = 10

The persons who are interested in photography but not in music and swimming is given by

$\Rightarrow P\left ( ph\cup  {s}' \cup {m}'  \right )=P\left ( ph \right )-P\left ( ph \cap s \right )-P\left ( p \cap m \right )+P\left ( p \cap s \cap m \right )$

$\Rightarrow P\left ( ph\cup  {s}' \cup {m}'  \right )=70-20-40+10$

$\Rightarrow P\left ( ph\cup  {s}' \cup {m}'  \right )=20$

There are 20 persons who are interested in photography but not in music and swimming.

Answer 2

Answer:

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