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In a class of 25 students, 15 of them have a cat , 16 of them have a dog and 3 of them have neither. Find the probability that a student chosen at random has a cat and a dog. Find the probability that a student chosen at random has a cat and a dog

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kudzordzifrancis

ANSWER

[tex] \frac{9}{25} [/tex]

EXPLANATION

The given information is represented on the Venn diagram above, where x represents students who have both cat and dog.

The sum of all the regions should give us 25.

[tex](15 - x) + x + (16 - x) + 3 = 25[/tex]

Group similar terms to obtain;

[tex] - x + x - x = 25 - 15 - 16 - 3[/tex]

Simplify

[tex] - x = - 9[/tex]

[tex]x = 9[/tex]

The probability that a student chosen at random has a cat and a dog is

[tex] = \frac{9}{25} [/tex]

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adioabiola

The probability that a student chosen at random has a cat and a dog is; P(cat and dog) = 9/25.

According to the question, the total number of students is; 25.

  • 15 of them have a cat

  • 16 of them have a dog

  • while, 3 of them have neither

The information above are drawn in a Venn diagram in the attached image.

  • where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

  • 15-x + x + 16-x + 3 = 25.

  • -x = 25 - 34

In essence, x = 9

  • Therefore, the number of students who own a cat and a dog is 9.

The probability that a student chosen at random has a cat and a dog is therefore;

  • P(cat and dog) = 9/25.

Read more;

https://brainly.com/question/1980403

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