Math Background

Probability: When Students Ask

  • How can I find all possible choices?
    Suppose you have a choice of 5 pizza toppings and 2 kinds of crust. To find all possible choices, multiply the number of possible toppings (5) by the number of crust choices (2); 5 x 2 = 10. If you want to list all the possible choices, you can make an organized list or draw a tree diagram.
tree diagram

This shows a picture of all the possible choices available to you when ordering a one-topping pizza.

  • What's the likelihood of an event occurring if the probability is one-half?
    The most common example of such an event is a coin toss. There are only two possible outcomes, heads or tails, and each outcome is equally likely to occur. The probability of the coin landing on heads or tails is 1 out of 2, or one-half.
  • What is meant by “zero probability? ” What is meant by “a probability of one?”
    Consider rolling a 1-6 number cube. The probability of rolling the cube and having an 8 land faceup is zero-sixths, or 0. Since that outcome is impossible, the probability of rolling an 8 is zero. The probability of rolling the same cube and getting a number less than 7 is six-sixths, or one. Therefore, the probability of rolling a number less than 7 is one, since the outcome is certain.
  • How do I know if my numerator and denominator are correct when I write a probability as a fraction?

    The numerator should represent the favorable outcomes. The denominator should represent all the possible outcomes. Use the spinner below an example.


What is the probability of spinning and landing on a number less than 6? Since the spinner is divided into 8 equal sections, there are 8 equally likely outcomes. Since there are 3 sections with numbers less than 6, there are 3 out of 8 chances that the spinner will land on a number —1, 3, or 5— less than 6. So the probability of the event is written as three-eighths: the numerator (3) is the number of favorable outcomes, and the denominator (8) is the number of possible outcomes.

  • When tossing a coin, if I get heads 3 times in a row, will I be more likely to get tails on my fourth toss?
    Remind students that every time a fair coin is tossed, the probability of getting either heads or tails is always one-half. The fourth toss isn't affected by what happened on the first three tosses. Each toss is an independent event.

Houghton Mifflin Math Grade 5