Mathematics
Intermediate Mathematical Challenge
2023
20

20

I roll two standard six-sided fair dice. At least one of the scores obtained on the dice is 3. What is the probability that both of the scores on the dice are 3?

A. 1/12

B. 1/11

C. 1/6

D. 1/3

E. 1/4

Answer

B. 1/11

SOLUTIOn

There are 36 different equally likely possible outcomes (a, b) for the two dice. The number of these which involve only 1, 2, 4, 5 or 6 is 5 × 5 = 25.

So there are just eleven involving a 3, one of which is (3, 3).

So the probability that both are 3, given that at least one is 3, is 1/11.

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FAQ

Find quick answers to common questions about our lessons, pricing, scheduling, and how Exact Science can help your child excel.
Where do you hold your classes?
We hold our classes online or on-site on Saturdays at our branch in Pimlico Academy, London.
You can find our timetable here.
What do you need to start learning online?
For lessons you only need a computer or phone with a microphone, camera and Internet access. Wherever you are - in London, Nottingham, New York or Bali - online lessons will be at hand.
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What should I expect from the trial lesson?
The trial lesson is a 30-minute online session designed to get a sense of how your child approaches mathematical thinking and problem solving. (In practice, it often runs a bit longer if the student is engaged!)

We typically explore a range of fun and challenging problems drawn from competitions. We adapt the difficulty based on how the student responds, aiming to make it both accessible and stimulating.

After the session, we’ll have a quick conversation with the parent to share observations and suggest a personalised path forward.
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It is OK, it happens! Students have the opportunity to cancel a lesson up to 8 hours before the scheduled time without loss of payment. So you can reschedule it for a convenient time, and the teacher will have the opportunity to
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