Question

NO LINKS!!! THIS IS NOT MULTIPLE CHOICE!!!
When you list all of the possible outcomes in a sample space by following an organized system (an orderly process), it is called a systematic list. There are different strategies that may help you make a systematic list, but what is most important is that you methodically follow your system until it is complete.
To get home, Renae can take one of 4 buses: #41, #28, #55, or #81. Once she is on a bus, she will randomly select one of the following equally likely activities: listening to her MP3 player, writing a letter, or reading a book.

a. Create the sample space of all possible ways Renae can get home and do one activity by making a systematic list.

b. Use your sample space to find the following probabilites:
i. P(Renae takes an odd-numbered bus)
ii. P(Renae does not write a letter)
iii. P(Renae catches #28 bus and then reads a book)

c. Does her activity depend on which bus she takes? Explain why or why not.

Answer 1

Answer:

Part (a)

see attached for sample space

Part (b)

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Total number of possible outcomes = 12

$\textsf{P(Renae takes an odd-numbered bus)}= \dfrac{9}{12}=\dfrac34$

$\textsf{P(Renae does not write a letter)}= \dfrac{8}{12}=\dfrac23$

$\textsf{P(Renae catches no.28 bus then reads a book)}= \dfrac{1}{12}$

Part (c)

Her activity does not depend on which bus she takes, as we have been told that once she is on the bus, she randomly selects the activity.  Therefore, the activity selection is independent from the bus selection.

The sample space confirms this as it shows that the probability of the selecting each activity is equally likely for each of the 4 buses.