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