TalkingPencil

Calculate a probability by listing the sample space and counting

Follow this one with me, a step at a time. Try to guess each step first.
Worked example 1

Each of two boxes holds 5 cards numbered 1 to 5. One card is drawn at random from each box. Find the probability that the sum of the two numbers is 3.

Remember: List the outcomes in a table: there are 5 × 5 of them, and each is equally likely. (1, 2) and (2, 1) are different outcomes.

Common mistakes

  • Counted (1, 2) and (2, 1) as one outcome. They are different outcomes.
  • Treated each possible total as equally likely. Outcomes are equally likely and totals are not, so list the outcomes.
  • Added the two sets of outcomes. Each outcome of the first pairs with every outcome of the second, so they multiply.