In a group of 25 students, 6 study both Art and Biology. 10 study Biology but not Art. 3 study neither subject. Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?

Probability that the student studies Art and biology is; P(A n B) = ½

We are given;

Total number of students in the group; n = 25 students

Number that study both art and biology; n(A u B) = 6

Number that study biology but not art; n(B u A') = 10

Number that study none of the 3 subjects; n(A' u B') = 3

Now;

Number that study only arts is; n(A n B') = 25 - 6 - 10 - 3 = 6

Since n(A u B) = 6

Then;

n(A) = n(A u B) + n(A n B')

n(A) = 6 + 6

n(A) = 12

Thus;

Probability that the student studies Art and biology is;

P(A n B) = 6/12

P(A n B) = ½

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1/2

Step-by-step explanation:

There are a total of 25 students. 3 don't study art or biology. 10 study only biology. 6 study both art and biology. This means the remaining students only study art.

1. Calculate the number of students taking art

only art: 25 - 3 - 6 - 10 = 6

number of students taking art and biology: 6

total number of students taking art: 12

2. Calculate the probability

Out of the 12 total students taking art, 6 are in art and biology.

6/12 = 1/2  

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.