A worker will drive through two sets of traffic lights on their way to work.
The probability of the first set of traffic lights being on green is
.
The probability of the second set of traffic lights being on green is
.
Draw and label a tree diagram including the probabilities of all possible outcomes.
Both sets of lights will either be on green (G) or red (R) (we can ignore yellow/amber for this situation).
We know the probabilities of the traffic lights being on green, so need to work out the probabilities of them being on red.
We also need to work out the combined probabilities of both traffic lights.
Find the probability that both sets of traffic lights are on red.
As we have written the probabilities of the combined events we can write the answer straight down.
Find the probability that at least one set of traffic lights are on red.
This would be " R AND G" OR " G AND R" OR " R AND R" so we need to add three of the final probabilities.
Because 'at least one R' is the same as 'not both G', we can also calculate this by subtracting P( G, G) from 1.
Liana has 10 pets
7 guinea pigs (G) and 3 rabbits (R).
Liana is choosing two pets to feature in her latest online video. First she is going to choose at random one of the pets. Once she has carried that pet to her video studio she is going to go back and choose at random a second pet to also feature in the video.
Draw and label a tree diagram including the probabilities of all possible outcomes.
For the 1st pet chosen, there will be a 7/10 probability of choosing a guinea pig, and a 3/10 probability of choosing a rabbit.
If the first pet is a guinea pig, there will only be 6 guinea pigs and 3 rabbits left (9 animals total). So for the second pet the probability of choosing a guinea pig would be 6/9, and probability of choosing a rabbit would be 3/9.
If the first pet is a rabbit, there will only be 7 guinea pigs and 2 rabbits left (9 animals total). So for the second pet the probability of choosing a guinea pig would be 7/9, and probability of choosing a rabbit would be 2/9.
Put these probabilities into the correct places on the tree diagram, and then multiply along the branches to find the probabilities for each outcome.
Find the probability that Liana chooses two rabbits.
As we have already calculated this probability in the table, we can just write the answer down.
Find the probability that Liana chooses two different kinds of animal.
This would be "G AND R" OR "R AND G" so we need to add two of the final probabilities.