1.3. Dependent Events and Sample Spaces http://www.ck12.org
Guided Practice
Meg bought a box of chocolates that contained 18 caramels, 8 chocolate-covered cherries, and 14 truffles. What is
the probability of Meg reaching into the box and pulling out a chocolate-covered cherry and then reaching in again
and pulling out a caramel or a truffle? Assume that the chocolate-covered cherry is not replaced. What if the order
were switched? In other words, what is the probability of Meg reaching into the box and pulling out a caramel or a
truffle and then reaching in again and pulling out a chocolate-covered cherrywithout replacement?
Answer:
Since there is a total of 18+ 8 + 14 =40 chocolates in the box, the probability that Meg first pulls out a chocolate-
covered cherry is 408 =^15. At this point, since the chocolate-covered cherry is not replaced, there are 40− 1 = 39
chocolates remaining in the box. Of those 39 chocolates, 18+ 14 =32 are either a caramel or a truffle. Therefore,
the probability that Meg pulls out a caramel or a truffle after first pulling out a chocolate-covered cherry is^3239.
Now that we know the probability of Meg first pulling out a chocolate-covered cherry and the probability of Meg
then pulling out a caramel or a truffle, we can calculate the probability of both of these events happening. To do this,
we can use the Multiplication Rule as follows:
P(chocolate-covered cherry)×P(caramel or truffle) =1
5
×
32
39
=
32
195
If the order were switched, the probability that Meg first pulls out a caramel or a truffle is^3240 =^45 , and the probability
that Meg then pulls out a chocolate-covered cherry is 398. Therefore, the probability of both events occurring can be
calculated with the Multiplication Rule as follows:
P(caramel or truffle)×P(chocolate-covered cherry) =4
5
×
8
39
=
32
195
Thus, the probability is the same, regardless of the order.
Practice
- Determine which of the following are examples of dependent events.
a. Selecting a marble from a container and selecting a jack from a deck of cards.
b. Rolling a number less than 4 on a die and rolling a number that is even on the same roll.
c. Choosing a jack from a deck of cards and choosing another jack, without replacement. - Determine which of the following are examples of dependent events.
a. Selecting a book from the library and selecting a book that is a mystery novel.
b. Rolling a 2 on a die and flipping a coin to get tails.
c. Being lunchtime and eating a sandwich. - Thomas bought a bag of jelly beans that contained 10 red jelly beans, 15 blue jelly beans, and 12 green jelly
beans. What is the probability of Thomas reaching into the bag and pulling out a blue or green jelly bean and
then reaching in again and pulling out a red jelly bean? Assume that the first jelly bean is not replaced. - For question 3, what if the order were reversed? In other words, what is the probability of Thomas reaching
into the bag and pulling out a red jelly bean and then reaching in again and pulling out a blue or green jelly
beanwithout replacement? - What is the probability of drawing 2 face cards one after the other from a standard deck of cardswithout
replacement?