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Prerequisites

# Theoretical probability

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There are 400 seats in a cinema theatre, numbered from 1 to 400. You buy a movie ticket and are allocated a seat. You have an equal chance of being allocated to each seat. Are you

**more**likely to be allocated to a seat numbered under 200 than a seat numbered over 200?**less**likely to be allocated to a seat numbered under 200 than a seat numbered over 200?**equally**likely to be allocated to a seat numbered under 200 as a seat numbered over 200?

You pick a date at random from this calendar year. Each date is equally likely to be picked. Is the probability that the date you pick falls on a Monday going to equal precisely \(\dfrac{1}{7}\)? Explain your answer.

Hover for answer: No; the number of days in the year is not divisible by 7.

A bag contains only red, green, and blue marbles. Assuming marbles are well-mixed, the probability of picking a green marble is double the probability of picking a red marble, and the probability of picking a blue marble is three times the probability of picking a green marble.

- What is the lowest possible number of marbles in the bag?
- What is the second lowest possible number of marbles in the bag?
- What is the third lowest possible number of marbles in the bag? What do you notice?
- 9 marbles
- 18 marbles
- 27 marbles; total number must be a multiple of 9

Hover for answers:

In the real world

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