Homework #3 -- Suggested Answers

 

ISBE 3.4, 3.5, 3.7, 3.10, 3.12, 3.13, 3.33, 3.34

 

 

3.4

  1. 12% + 12% + 12% = 36%
  2. 3*(12%) + 11% = 47%
  3. 1 - (14% + 11%) = 75%
  4. 13% + 12% = 25%

 

3.5

  1. a) Learning experiment, 2 tasks in a row:

  2. b) Learning experiment, 3 tasks in a row:

 

3.7

  1. (8/12)*(7/11)*(6/10) = 25.45%
  2. (6/12)*(5/11)*(4/10) = 9.09%

 

3.10

  1. 10% + 6% - 2% = 14%
  2. 100% - 14% = 86%
  3. 6% - 2% = 4%

 

3.12

  1. 17% + 23% = 40%
  2. 38% + 22% = 60%
  3. 17% + 38% = 55%
  4. 100% - 22% = 78%
  5. 17%
  6. 17%/40% = 42.5%; 23%/40% = 57.5%

 

3.13

The Venn diagram:

  1. .02+.03+.03+.08+.17+.12+.07 = .52
  2. .17
  3. .52-.12 = .40
  4. .17/.52 = .33
  5. .40/.52 = .77

 

3.33

  1. Yes
  2. Yes
  3. Yes

 

3.34

  1. Chance = 1/4, odds = 1/3
  2. Chance = 1/2, odds = 1/1
  3. Chance = 1/13, odds = 1/12
  4. Chance = 4/13, odds = 4/9
  5. Chance = 3/51, odds = 3/49
  6. Chance = 24/51, odds = 24/27. (It can be higher, lower or the same. In part e we saw that the probability it is the same is 3/51, hence the probability that it is higher or lower is 48/51. There are as many ways of drawing 2 cards the first lower than the second as there are ways of drawing 2 cards the first higher than the second, therefore the probability that the card is higher than the next is half of 48/51 or 24/51. This calculation can also be done by conditioning on the value of the first card.)