Suppose that of 1400 students, 550 take Spanish, 700 take biology, and 400 take both

Spanish and biology. What is the probability that a student selected at random takes

Spanish or Biology? Simplify the fraction!

17/28

Explanation:

1. Call A the event of selecting a student who takes Spanish and P (A) the corresponding probability:

P (A) = number of students who take Spanish / number of students

P (A) = 550 / 1400 = 11/28

2. Call B the event of selecting a student who takes biology and P (B) the corresponding probability:

P (B) = number of students who take biology / number of students

P (B) = 700 / 1,400 = 1/2

3. The joint probability, P (A∩B), is the probability that a student takes Spanish and biology:

P (A∩B) = number of students that take both Spanish and biology / number of students

P (A∩B) = 400/1400 = 2/7

4. By the properties of probabilities, the probability of the event A or B is:

P (A or B) = P (A∪B) = P (A) + P (B) - P (A∩B)

P (A or B) = 11/28 + 1/2 - 2/7 = (11 + 14 - 8) / 28 = 17/28