ProbabilityIB MYP Maths Extended: Topic test

1. 1
   A game at a school fair in Lima uses a fair spinner with $8$ equal sections numbered $1$ to $8$.

   (a)

   The spinner is spun once. What is the probability of landing on a prime number?

   [1 mark]

   • A$\frac14$
   • B$\frac38$
   • C$\frac12$
   • D$\frac58$

   (b)

   The spinner is spun once. What is the probability of NOT landing on a multiple of $3$?

   [1 mark]

   • A$\frac34$
   • B$\frac14$
   • C$\frac78$
   • D$\frac58$

   (c)

   The spinner is spun twice and the two scores are added. Find the probability that the total is $9$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A weather station in Reykjavik recorded rain on $54$ of the $180$ days of one season.

   (a)

   What is the relative frequency of a rainy day in this season?

   [1 mark]

   • A$0.7$
   • B$3.3$
   • C$54$
   • D$0.3$

   (b)

   Using this relative frequency as the probability of rain, how many rainy days would be expected in a season of $90$ days?

   [1 mark]

   • A$54$
   • B$27$
   • C$63$
   • D$30$

   (c)

   A second station records rain on $408$ of $1200$ days, a relative frequency of $0.34$. Which station gives the better estimate of the probability of rain? Give a reason.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A bakery in Vienna asks $60$ customers what they bought. Of these, $34$ bought bread, $28$ bought cake and $9$ bought neither.

   (a)

   How many customers bought both bread and cake?

   [3 marks]

   (b)

   A customer is chosen at random. Find the probability that the customer bought exactly one of the two items.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A nursery in Costa Rica finds that $8\%$ of its plants have a disease. A test gives a positive result for $90\%$ of diseased plants and for $5\%$ of healthy plants.

   (a)

   A plant is chosen at random.
   (i) Show that the probability that the plant is diseased and tests positive is $0.072$.
   (ii) Find the probability that the plant tests positive.

   [6 marks]

   (b)

   (i) A plant tests positive. Find the probability that it is diseased.
   (ii) The nursery tests $2000$ plants. Estimate how many test positive.
   (iii) Comment on what a positive test result tells the nursery.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   A student in Nairobi flips a fair coin three times and records heads (H) or tails (T) each time.

   (a)

   What is the probability of getting three heads?

   [1 mark]

   • A$\frac18$
   • B$\frac12$
   • C$\frac13$
   • D$\frac38$

   (b)

   What is the probability of getting exactly two heads?

   [1 mark]

   • A$\frac18$
   • B$\frac14$
   • C$\frac38$
   • D$\frac12$

   (c)

   Find the probability of getting at least one tail.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   A student in Rotterdam cycles to school every day. On any day, independently of other days, the probability that she arrives late is $0.1$.

   (a)

   What is the probability that she is late on both Monday and Tuesday?

   [1 mark]

   • A$0.2$
   • B$0.01$
   • C$0.1$
   • D$0.19$

   (b)

   What is the probability that she is late on exactly one of the two days?

   [1 mark]

   • A$0.09$
   • B$0.01$
   • C$0.19$
   • D$0.18$

   (c)

   Find the probability that she is late at least once from Monday to Wednesday.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   At a charity raffle in Nairobi, $12$ tickets are in a drum and $3$ of them win a prize. Two tickets are drawn one after the other without replacement.

   (a)

   Find the probability that both tickets win a prize.

   [3 marks]

   (b)

   Find the probability that at least one of the two tickets wins a prize.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   A gym in Nairobi has $80$ members. Of these, $48$ use the pool, $36$ go to classes and $14$ do both.

   (a)

   (i) Find the number of members who use neither the pool nor classes.
   (ii) A member is chosen at random. Given that the member uses the pool, find the probability that the member also goes to classes.

   [6 marks]

   (b)

   Two different members are chosen at random.
   (i) Find the probability that both use the pool.
   (ii) The first member chosen goes to classes. Find the probability that the second member uses neither the pool nor classes.
   (iii) Are the events "the first member uses the pool" and "the second member uses the pool" independent? Justify your answer.

   [6 marks]

   Total for question 8: 12 marks

End of questions