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/b/

jmaths

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

Fair games and further distributions Problem set B Answers

Skills

    1. (a) £2.50
    2. (b) Yes, fair: expected gain is 0
    1. (a) x = 0, 1, 2, 3: 1/11, 3/22, 3/11, 1/2
    2. (b) 24/11 = 2.18
    1. (a) x = 2, 3, 4, 5, 6, 7, 8, 9: 1/20, 1/10, 3/20, 1/5, 1/5, 3/20, 1/10, 1/20
    2. (b) 5.5
    1. (a) 0.441
    2. (b) x = 0, 1, 2, 3: 0.027, 0.189, 0.441, 0.343
    3. (c) 2.1
    1. (a) x = 0, 1, 2: 7/15, 7/15, 1/15
    2. (b) 3/5 = 0.6
    1. (a) x = 0, 1, 2, 3, 4: 1/5, 8/25, 6/25, 4/25, 2/25
    2. (b) 1.6

In context

    1. (a) $0.60
    2. (b) −$0.40: not fair
    3. (c) $40.00

  2. n = $3.00

    1. (a) k = 1/20
    2. (b) 11/20
    3. (c) 3/2 = 1.5

Stretch

    1. (a) a + b = 0.55 and a + 2b = 0.95
    2. (b) a = 0.15, b = 0.4
    1. (a) c = 1/54
    2. (b) 41/50 = 0.82
    3. (c) 112/27 = 4.15

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