Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-sl/probability-distributions/13-2-3/problems/

jmaths

IB Mathematics: Applications and Interpretation SL · 13.2: Probability Distributions · 13.2.3

Fair games and further distributions Problem set A Answers

Skills

    1. (a) $1.50
    2. (b) Yes, fair: expected gain is 0
    1. (a) x = 0, 1, 2, 3: 1/18, 1/9, 5/18, 5/9
    2. (b) 7/3 = 2.33
    1. (a) x = 2, 3, 4, 5, 6, 7: 1/12, 1/6, 1/4, 1/4, 1/6, 1/12
    2. (b) 4.5
    1. (a) 0.288
    2. (b) x = 0, 1, 2, 3: 0.216, 0.432, 0.288, 0.064
    3. (c) 1.2
    1. (a) x = 0, 1, 2: 188/221, 32/221, 1/221
    2. (b) 2/13 = 0.154
    1. (a) x = 0, 1, 2, 3: 1/4, 3/8, 1/4, 1/8
    2. (b) 1.25

In context

    1. (a) $1.05
    2. (b) −$0.95: not fair
    3. (c) $190.00

  2. n = $2.00

    1. (a) k = 1/15
    2. (b) 3/5
    3. (c) 4/3 = 1.33

Stretch

    1. (a) a + b = 0.65 and a + 3b = 1.55
    2. (b) a = 0.2, b = 0.45
    1. (a) c = 1/30
    2. (b) 25/29 = 0.862
    3. (c) 10/3 = 3.33

jmaths.xyz · AI SL · 13.2.3 Fair games and further distributions