3.8 Interactive double coin toss

The example below displays the probability and expected frequency trees for the double coin toss. If the plots are not displaying correctly, then please refresh your page. You can view this example and others in our online application. Use the sliders below to change the probability of a head for both coins and also the number of double tosses for the expected outcomes. Here is an activity to try:

The multiplication rule for independent events states that the probability of two independent events both occurring can be obtained by multiplying the probability of each independent event together. Verify that this probability model for the double coin toss satisfies the multiplication rule by:

• Finding the probability for double heads on the probability tree and checking that it equals the probability of a head multiplied by itself. (Use an online calculator if needed!)
• Working out the probability of tails from the probability of heads. (Hint: they are exhaustive and mutually exclusive.)
• Finding the probability for double tails on the probability tree and checking that it equals the probability of a tail from the previous step multiplied by itself.
• Finding the probability of a coin 1 head with a coin 2 tail on the probability tree and checking that it equals the probability of a head multiplied by the probability of a tail. (This is the same for a coin 1 tail with a coin 2 head.)
• Changing the probability of a head to another number and repeating the previous steps once more.