c Highlight all the paths in the tree diagram where a photo of the niece is not included.
A
a See diagram.
B
b P(both on boyfriend)=1/4
C
c P(neither on niece)=5/6
Practice makes perfect
a To draw the tree diagram, we first need to determine the probability of her phone showing each type of photo. To calculate probability, we divide the number of favorable outcomes by the number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomes
From the exercise, we know that 2 photos are of her parents, 1 is of her niece and 3 are of her boyfriend for a total of 6 photos. Now we can determine the probability of each type of photo showing up when she turns on the phone.
P(parents)&=2/6 [0.8em]
P(niece)&=1/6 [0.8em]
P(boyfriend)&=3/6
When we know all probabilities, we can draw our tree diagram.
b Let's first highlight the path through the tree diagram that shows both pictures being of her boyfriend.
c Let's highlight the paths in the tree diagram where neither photo is of her niece.
To calculate each of these probabilities, we have to use the Multiplication Rule of Probability.
P(parents,parents):& 2/6* 2/6=4/36 [0.8em]
P(parents,boyfriend):& 2/6* 3/6=6/36 [0.8em]
P(boyfriend,parents):& 3/6* 2/6=6/36 [0.8em]
P(boyfriend,boyfriend):& 3/6* 3/6=9/36
By adding these probabilities, we get the probability that neither of the photos are of her niece
