Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/probability/13-1-7/problems/b/

jmaths

IB Mathematics: Applications and Interpretation HL · 13.1: Probability · 13.1.7

Name Date

Independent events Problem set B

Show every step. Give probabilities as fractions or decimals, and use a sample space diagram or Venn diagram where the question asks.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. On a school day, the probability that the lift is out of order is 0.55 and the probability that the canteen card machine is out of order is 0.3. The two faults are independent. Find the probability that both are out of order on the same day.

  2. For events A and B, \(P(A)=0.3\), \(P(B)=0.6\) and \(P(A\cup B)=0.75\). Determine whether A and B are independent. Justify your answer.

  3. A bike's front light and its rear light fail independently. The probability that the front light fails is 0.2. The probability that both fail is 0.09. Find the probability that the rear light fails.

  4. Events A and B are independent, with \(P(A)=\frac{5}{9}\) and \(P(A\cap B)=\frac{10}{27}\). Find \(P(B)\).

  5. Events C and D have P(C) = 0.4 and P(D) = 0.3.

    1. (a) C and D are independent. Find P(C ∪ D).
    2. (b) State, with a reason, whether C and D could also be mutually exclusive.

In context

  1. At a school fair, two fair six-sided dice are rolled and the prize depends on the product of the two numbers.

    1. (a) Use a sample space diagram to find the probability that the score is at most 6.
    2. (b) The game is played 108 times. How many times would you expect the score to be at most 6?

  2. A game uses a fair four-sided die (numbered 1 to 4) and a fair eight-sided die (numbered 1 to 8). The two scores are added to give the total.

    1. (a) Find the probability that the total is 8.
    2. (b) Find the probability that the total is a multiple of 3.

  3. Of 160 residents of a street, 70 own a car, 55 own a bicycle and 25 own both.

    1. (a) Draw a Venn diagram to show this information.
    2. (b) Find the probability that a person chosen at random does neither.
    3. (c) Find the probability that a resident owns a car, given that they do not own a bicycle.

  4. A fair 12-sided die is numbered 1 to 12 and rolled once. M is the event "the score is a multiple of 3" and E is the event "the score is even".

    1. (a) Are M and E mutually exclusive? Give a reason.
    2. (b) Are M and E independent? Show your working.

Stretch

  1. Two events are independent, with \(P(A)=0.4\) and \(P(B)=0.25\). Find \(P(A\cup B)\).

  2. Events A and B are independent, with \(P(A)=0.7\) and \(P(A\cup B)=0.91\). Find \(P(B)\).

jmaths.xyz · AI HL · 13.1.7 Independent events