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.

spinner

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