Probabilities for four spins of a biased spinner, then the expected number of blues and the expected score in a points game

Probabilities for four spins of a biased spinner, then the expected number of blues and the expected score in a points game

10 marks

A spinner is biased so that, on each spin, it lands on blue with probability \(\frac14\). The results of different spins are independent.

  1. The spinner is spun four times. Find the probability that it lands on blue
    1. on all four spins;
    2. on exactly one of the four spins.[5]
  2. In a game, the spinner is spun \(20\) times.
    1. Write down the expected number of times that the spinner lands on blue.
    2. A player scores \(9\) points each time the spinner lands on blue and loses \(2\) points each time it does not. Find the player's expected score.[5]

Solution:

Solution locked

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.

Create a free account to practise similar questions.

Answer:(a)(i) \(\dfrac{1}{256}\) (a)(ii) \(\dfrac{27}{64}\) (b)(i) \(5\) (b)(ii) \(15\) points

Need help? Join our JC Math tuition classes.

Learn more