P2a – Theoretical probability

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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?
Hover for answer:   less likely to be allocated a seat numbered under 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.
  1. What is the lowest possible number of marbles in the bag?
  2. What is the second lowest possible number of marbles in the bag?
  3. What is the third lowest possible number of marbles in the bag? What do you notice?
  4. Hover for answers:

    1.   9 marbles
    2.   18 marbles
    3.   27 marbles; total number must be a multiple of 9
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