Chapter Objectives

  • Understand and use the terminology of probability
  • Determine whether two events are mutually exclusive and whether two events are independent
  • Calculate probabilities using the addition rules and multiplication rules
  • Construct and interpret contingency tables
  • Construct and interpret Venn diagrams
  • Construct and interpret tree diagrams

Assignment

This lesson is applying the probability rules you’ve learned to two-way tables, which you saw first in section 1.2. So, no slides this time. Instead, we’ll do an example from the book.

  Speeding Violation
in the Last Year		 No Speeding Violation
in the Last Year		 Total
Uses a cell phone while driving 25 280 305
Does not use a cell phone while driving 45 405 450
Total 70 685 755

  1. Find P(Person uses a cell phone while driving).

    Out of the 755 people in the survey, 305 used a cell phone while driving, so $305/755\approx0.4$.

  2. Find P(Person had no violation in the last year).

    Again, 755 people in the survey, but this time 685 has no violations. $685/755\approx0.91$.

  3. Find P(Person had no violation in the last year AND uses a cell phone while driving).

    You can do this with the formula for “and” events $P(A)P(B|A)$. The probability of no violations we found already, and using a cell phone while also not getting a violation is $280/685$. Multiplying the two you get about $0.37$.

    But the nice thing about contingency tables is that “and” events can be found directly. Out of the 755 people, 280 fall into both categories. $280/755\approx0.37$.

  4. Find P(Person uses a cell phone while driving OR person had no violation in the last year).

    Here, you can’t get away from the formula $P(A)+P(B)-P(A \text{ and } B)$. Add up the two categories and subtract the overlap. Luckily, the conditional probability is easy to get since we are dealing with a contingency table.

    $305/755 + 685/755 - 280/755\approx0.94$