Exercise 56 Page 172

a List:

Bus #41: Listening to MP3
Bus #41: Writing a letter
Bus #41: Reading a book
Bus #28: Listening to MP3
Bus #28: Writing a letter
Bus #28: Reading a book
Bus #55: Listening to MP3
Bus #55: Writing a letter
Bus #55: Reading a book
Bus #81: Listening to MP3
Bus #81: Writing a letter
Bus #81: Reading a book

Practice makes perfect

a There are four buses that Renae can take, #41, #28, #55, and #81. On the buses, she can do one of three activities. We can illustrate this with the following sample space.

Let's organize the sample space into a list. For each bus she can take, she can do three activities. Therefore, the list will have a total of 12 outcomes. Bus #41:& Listening to MP3 Bus #41:& Writing a letter Bus #41:& Reading a book Bus #28:& Listening to MP3 Bus #28:& Writing a letter Bus #28:& Reading a book Bus #55:& Listening to MP3 Bus #55:& Writing a letter Bus #55:& Reading a book Bus #81:& Listening to MP3 Bus #81:& Writing a letter Bus #81:& Reading a book

b To determine probability, we divide the number of favorable outcomes with the number of possible outcomes.

P=Number of favorable outcomes/Number of possible outcomes

i. P(Renae takes an odd numbered bus)

Examining the numbers, we see that three of them are odd numbers.

#41, #55 and #81 This means 3 out of 4 outcomes are favorable and, therefore, the probability of taking an odd-numbered bus is 34 or 75 %.

ii. P(Renae does not write a letter)

Note that the number of the bus does not matter here. Any outcome that results in Renae not writing a letter is a favorable outcome. Let's highlight all of the favorable outcomes in our sample space.

There are 8 favorable outcomes out of 12 total outcomes. Therefore, the probability of Renae not writing a letter is 812= 23 or about 67 %.

iii. P(Renae catches the #28 bus and then reads a book)

Again, let's highlight the favorable outcomes in our sample space.

In this case, there is only 1 favorable outcome out of 12 total outcomes. Therefore, the probability of Renae taking the 28 bus and then reading a book is 112 or about 8 %.

c No, the bus she steps onto does not influence the activity she chooses to do. These are independent events which means the probability that one event occurs does not affect the probability of another event occurring.