1. 12.4 Multiplying Probabilities, II
Dependent Events

2. Probability of 2 Dependent Events
If two events, A and B, are dependent, then the probability of both events occurring is 𝑃 𝐴 𝑎𝑛𝑑 𝐵 =𝑃 𝐴 ∗𝑃(𝐵 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝐴)
Recall: Independent events – current choices affect future choices.

3. Example – Two Dependent Events
The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability.
A vacation, then a car.
A –
B –
𝑃 𝐴 =
𝑃 𝐵 =
𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

4. Example – Two Dependent Events
The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability.
A vacation, then a car.
A – first selection is vacation
B – second selection is car
𝑃 𝐴
𝑃 𝐵 =
𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

5. Example – Two Dependent Events
The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability.
A vacation, then a car.
A – first selection is vacation
B – second selection is car
𝑃 𝐴 =3/10
𝑃 𝐵 =
𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

6. Example – Two Dependent Events
The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability.
A vacation, then a car.
A – first selection is vacation
B – second selection is car
𝑃 𝐴 =3/10
𝑃 𝐵 =1/9
𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

7. Example – Two Dependent Events
The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability.
A vacation, then a car.
A – first selection is vacation
B – second selection is car
𝑃 𝐴 =3/10
𝑃 𝐵 =1/9
𝑃 𝐴 𝑎𝑛𝑑 𝐵 = = 1 30

8. Example 2– Two Dependent Events
The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability.
Two televisions.
A –
B –
𝑃 𝐴 =
𝑃 𝐵 =
𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

9. Example 2– Two Dependent Events
The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability.
Two televisions.
A – first selection is television
B – second selection is television
𝑃 𝐴 =6/10
𝑃 𝐵 =5/9
𝑃 𝐴 𝑎𝑛𝑑 𝐵 = = 1 3

10. Example
Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order.
A –
B –
C –

11. Example
Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order.
A – First card is diamond
B – Second card is club
C – Third card is diamond

12. Example
Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order.
A – First card is diamond
B – Second card is club
C – Third card is diamond

13. Example
Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order.
A – First card is diamond
B – Second card is club
C – Third card is diamond

14. Example
Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order.
A – First card is diamond
B – Second card is club
C – Third card is diamond

15. Example
Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order.
A – First card is diamond
B – Second card is club
C – Third card is diamond

16. Assignment

17. HW