Conditional Probability and Pebble World Intuition

Evidence shrinks the world

Computing with the definition

Conditional probability as a probability measure

In the class survey above, 120 students study calculus, of whom 72 study physics; of the 80 who do not study calculus, 24 study physics. What is P(studies calculus given studies physics)?

A screening test for a rare disease correctly lights up 99 percent of sick people. A journalist writes that a positive result means a 99 percent chance of disease. What is swapped?

Two fair dice are rolled. Given that the first die shows 3, what is the probability that the total is at least 7? Write the answer as a fraction a/b in lowest terms and enter b.

In a company, 30 percent of employees code and 20 percent code AND design. Among coders, what fraction design? Enter a decimal like 0.67.

Three coins are tossed. Given that at least one shows heads, what is the probability that all three show heads? Enter a fraction like 1/7.

In your own words, state the most important definition, theorem or method of this lesson and explain what it says.