Combined events and tree diagramsIB MYP Maths Extended: Subtopic test

1. 1
   A spinner in a board game played in Nairobi lands on green with probability $0.3$ and on yellow with probability $0.7$. It is spun twice, and the two spins are independent.

   (a)

   Find the probability that both spins land on green.

   [1 mark]

   • A$0.6$
   • B$0.09$
   • C$0.3$
   • D$0.21$

   (b)

   Find the probability that exactly one of the two spins lands on green.

   [1 mark]

   • A$0.21$
   • B$0.49$
   • C$0.42$
   • D$0.58$

   (c)

   Find the probability that at least one spin lands on yellow.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In a dormitory in Seoul, a drawer contains $6$ black socks and $4$ white socks. Two socks are taken at random, one after the other, without replacement.

   (a)

   Find the probability that both socks are black.

   [1 mark]

   • A$\frac{9}{25}$
   • B$\frac{3}{5}$
   • C$\frac{5}{9}$
   • D$\frac{1}{3}$

   (b)

   Find the probability that the two socks are different colours.

   [1 mark]

   • A$\frac{8}{15}$
   • B$\frac{12}{25}$
   • C$\frac{4}{15}$
   • D$\frac{7}{15}$

   (c)

   Find the probability that both socks are white.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A basketball player in Manila scores each free throw with probability $0.7$, independently of her other throws. She takes three free throws.

   (a)

   Find the probability that she scores exactly two of the three throws.

   [3 marks]

   (b)

   Find the probability that she scores at least two of the three throws.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A box in a school workshop in Lagos contains $10$ batteries, of which $2$ are faulty. Two batteries are taken at random from the box.

   (a)

   The first battery is not put back before the second is taken. Find the probability that (i) both batteries are faulty, (ii) neither battery is faulty, (iii) exactly one battery is faulty.

   [6 marks]

   (b)

   Now suppose the first battery is put back before the second is taken. (i) Find the probability that both batteries are faulty. (ii) Explain why this is greater than your answer to (a)(i). (iii) A large store holds $1000$ batteries, of which $200$ are faulty. Two are taken without replacement. Calculate the probability that both are faulty, and justify whether the with-replacement model is a reasonable approximation here.

   [6 marks]

   Total for question 4: 12 marks

End of questions