Question

DEPENDENT EVENTS AND CONDITIONAL PROBABILITY a school of 1,000 students, 600 study physics, 300 study Calculus, and 100 study both. What is the probability that someone who does not study calculus studies physics? Give your answer as a decimal to one decimal place.

Answer 1

Explanation:

The probability that someone who does not study calculus studies physics is 0.5

Since there are 1000 students in the school and 600 study physics, 300 study Calculus, and 100 study both, we need to find the number of students that study only physics to find the probability that someone who does not study calculus studies physics.

Let x = number of students who study both = 100, y = number of students who studies only physics and z = number of students who studies only calculus.

Given that the number of students who study physics are 600, we have

x + y = 600 (1)

Also, given that the number of students who study calculus are 300, we have

x + z = 300 (2)

From (1)

y = 600 - x

y = 600 - 100

y = 500

So, the probability of students that study only physics = probability that someone who does not study calculus studies physics is

P(physics) = number of students studying only physics/total number of students

= 500/1000

= 5/10

= 0.5

So, probability that someone who does not study calculus and studies physics is 0.5