Each day the number of snacks decreases by 1, which affects the probability of picking an apple or yogurt the following day.
P(not 3 yogurts)=11/12 Tree Diagram: See solution.
Practice makes perfect
Before we can draw our tree diagram, we have to figure out the probability of picking either a yogurt or an apple for each of the days.
P=Number of favorable outcomes/Number of possible outcomes
Assuming that Stephen does not care if the apples are green or red, we have the following number of apples, yogurts, and total snacks.
Apples:& 5
Yogurt:& 5
Total snacks:& 10
Since we have 5 yogurts and 5 apples, the probability of picking either type of snack will be 510. Note that this is the same thing as 12, but we will keep the ratio as 510. This is because as the days goes by the number of snacks decreases, which affects the probability. With this information we can draw our tree diagram.
The probability of Stephen not getting three yogurts on three consecutive days is the same thing as Stephen getting at least 1 apple. We can calculate this by first finding the probability of getting three yogurts and then taking the complement of this. Let's highlight the path through the tree diagram where Stephen gets three yogurts.
The probability of getting three yogurts is the product of the probabilities along the path of the tree diagram.
P(3 yogurts): 5/10*4/9*3/8=60/720
When we know the probability of getting three yogurts, we can calculate the complement of this to find the probability of not getting three yogurts.
