Lesson 3

Explore

In Discover, you noticed the difference in probability when marbles were replaced versus when marbles were not replaced. Two events are independent if the outcome of one event has no influence on the outcome of the other event. With independent events, the number of possible outcomes remains the same throughout the experiment. Some examples of independent events include the following:

• You spin the spinner, like the one shown, twice. The result from the first spin is completely independent from the result of the second spin.
  
  
  
• Two cards are randomly selected from a standard deck of playing cards. After drawing the first card, it is returned to the deck. The second card is then drawn.
• Marbles are drawn from a bag and returned before the next draw.

Two events are dependent if the outcome of the first event influences the outcome of the second event. The number of possible outcomes is changed. Some examples of dependent events include the following:

• You call to make an appointment with the dentist and you select an appointment time. Your friend then calls the same dentist and selects an appointment time that is still available.
• At a fundraising event, a ticket is drawn. That ticket is awarded second prize and taped on the gift. Your ticket is still in the draw.
• Marbles are drawn from a bag and not returned before the next draw.

Watch the video “Identifying Independent Events” to see how independent or dependent events can be identified.

Self-Check 1