Exam-Style Question on Probability
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 11. This question is similar to one that appeared on an IB Studies paper in 2010. The use of a calculator is allowed.
Julie chooses a cake from a yellow box on a shelf. The box contains two chocolate cakes and three plain cakes. She eats the cake and chooses another one from the box. The tree diagram below represents the situation with the four possible outcomes where C stands for chocolate cake and P for plain cake.
(a) Write down the value of \(x\).
(b) Write down the value of \(y\).
(c) Find the probability that both cakes are plain.
On another shelf there are two boxes, one red and one green. The red box contains four chocolate cakes and five plain cakes and the green box contains three chocolate cakes and four plain cakes. Ben randomly chooses either the red or the green box and randomly selects a cake.
(d) Copy and complete the tree diagram below.
(e) Find the probability that he chooses a chocolate cake.
(f) Find the probability that he chooses a cake from the red box given that it is a chocolate cake.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
©1997 - 2022 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/