a Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes.
B
b Remember, the music player does not repeat a song that was already played.
C
c Cross out played songs from the list. How many songs are left? How many of these were recorded by Sapphire?
D
d Note that we are not looking for a combination of two events.
A
a P=2/5
B
b Yes, it does. See solution.
C
c 12, see solution.
D
d They are both 13.
Practice makes perfect
aProbability is calculated by dividing the number of favorable outcomes by the number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomes
In this case, there are 5 possible songs and 2 of them are country. With this information we can determine the probability that the first song is country.
P=2/5
b Yes, it affects the probability. From the exercise we know that the songs don't repeat. Therefore, when the second song comes on, the first song cannot play again. If the first song has played there are only 4 songs left, and 1 of them is country. This means the probability is affected.
c Let's list all of the songs and cross out those that have already played.
a. &I Love My Mama (country)
&by the Strings of Heaven
b. &Don't Call Me Mama (country)
&Duet by Sapphire and Hank Tumbleweed
c. &Carefree and Blue (R & B)
&by Sapphire and Prism Escape
d. &Go Back To Mama (Rock)
&Duet by Bjorn Free and Sapphire
e. &Smashing Lollipops (Rock)
&by Sapphire
There are two songs left in the playlist. Of these, one of them is a duet by Bjorn Free and Sapphire. Therefore, the probability that one of the songs is by Sapphire is 12.
d Let's draw a tree diagram representing the situation.
Note that we do not even have to consider what bus Renae takes. When she has stepped on a bus, the probability of each activity is equally likely. Therefore, the probability of writing a letter is 13, no matter what bus she takes.
This means the probability of Renae writing a letter is always 13, regardless of what bus she chooses.
