ANSWER
P(no eggs) = 67%
P(toast) = 33%
P(cereal and orange juice) = 17%
P(cereal or orange juice) = 83%
Step-by-step explanation
Aaron starts his day with either orange juice or apple juice followed by cereal, toast or scrambled eggs.
This means that he makes two sets of choices.
The first set is between Orange juice or apple juice.
The second set is between Cereal, Toast or Scrambled eggs.
a) The probability that Aaron chooses a breakfast with no eggs.
In the second set, there are 3 possible choices.
The probability of choosing a breakfast with eggs is:
P(eggs) = 1/3
So, the probability of choosing a breakfast with no eggs is:
P(no eggs) = 1 - 1/3
P(no eggs) = 2/3
In percentage:
P(no eggs) = 2/3 * 100
P(no eggs) = 67%
b) The probability that Aaron chooses a breakfast with toast.
The probability of choosing a breakfast with toast is:
P(toast) = 1/3
P(toast) = 1/3 * 100 (in percentage)
P(toast) = 33%
c) The probability that Aaron chooses a breakfast with cereal and orange juice.
To find this, we have to find the probability that he chooses a breakfast with cereal, the probability that he chooses a breakfast with orange juice and then find the product.
P(cereal) = 1/3
P(orange juice) = 1/2 (since he has two options in the first set)
So, the probability that he will choose a breakfast with cereal and orange juice is:
P(cereal and orange juice) = 1/3 * 1/2
P(cereal and orange juice) = 1/6
P(cereal and orange juice) = 1/6 * 100 (in percentage)
P(cereal and orange juice) = 17%
d) The probability that Aaron chooses a breakfast with cereal or orange juice.
To find this, we have to find the probability that he chooses a breakfast with cereal, the probability that he chooses a breakfast with orange juice and then add them together.
P(cereal) = 1/3
P(orange juice) = 1/2
P(cereal or orange juice) = 1/3 + 1/2
P(cereal or orange juice) = 5/6
P(cereal or orange juice) = 5/6 * 100 (in percentage)
P(cereal or orange juice) = 83%