At the beginning of this Training Camp , you saw examples of independent and dependent events. Two examples were as follows:

  • Pull a card from a standard deck, replace it, and pull a second card.

  • Pull a card from a standard deck and do not replace it before pulling a second card.

To distinguish between these examples when solving problems is important. If the objects in a problem are being replaced, then the events are independent. This could include replacing a marble into a bag, a card into a deck, or a person into a group. If the objects in a problem are not being replaced, then the events are dependent. For example, choose three people from a group of ten and not letting them rejoin the group, or select numbers for a lottery ticket if the numbers cannot be repeated.

With Replacement: The events are independent.

Without Replacement: The events are dependent.

What is the probability of drawing 2 aces from a standard deck if the first card is replaced before the second card is drawn?

Because the card is replaced, each draw is an independent event. A standard deck has 52 cards with 4 of each type of card. That means the probability of drawing an ace is .

The probability of drawing 2 aces with replacement is 0.59%.

 

You will see examples of finding probability without replacement later in the unit.

 

Read pages 193-194 Example 1 in your textbook, Principles of Mathematics 12 .

Complete the questions   on page 198 ( 2a & 2b) for more practice on determining the probability of independent events.

Click here to verify your answers .