Question

Assignment 3 Pathway: Business Ice Cream Flavors Chocolate Vanilla Strawberry Puthie Cake Batter Mint Chocolate Chip Rocky Road Bubble Gum Salted Caramel Other None Adult 33 24 24 12 23 Child 13 22 9 1 18 14 25 Total 16 Above is data for ice cream preferences of adults and children. The total for each flavor is found in the last row of the table. 1. Find the probability that the person preferred cake batter ice cream. 2. Find the probability that the person surveyed was a child. 3. Find the probability that the person preferred mint chocolate chip or rocky road ice cream. 4. Find the probability that the person preferred bubble gum ice cream, given the person surveyed was a child. 5. Find the probability that the person surveyed was an adult, given that they liked vanilla ice cream.

Answer 1

	Chocolate	Vanilla	Strawberry	Pistachio	Cake butter	Mint Chocolate Chip	Rocky Road	Bubble Gum	Salted Caramel	Other	None
Adult	33	24	24	17	25	23	20	27	22	14	6
Child	13	22	9	1	18	9	14	25	3	2	1
Total	46	46	33	18	43	32	34	52	25	16	7

Total no of persons= 46+46+33+18+43+32+34+52+25+16+7 = 352

Let P₁ and P₂ denote an adult and a child person.

Let F_i denote the i^th flavour of the ice-cream, i=1(1)11.

1) = P[F₅] = 43/352 = 0.122

2) The probability that the person surveyed was a child = (Total no. of children)/(Total no. of persons) = 117/352 = 0.332

3) The probability that the person preferred mint chocolate chip or rocky road ice-cream =

$P[F_{6}\cup F_{7}] =P[F_{6}]+P[F_{7}]-P[F_{6}\cap F_{7}]$

= (32/352) + (34/352)+0

= 0.1875

4) The probability that the person preferred Bubble gum ice cream given that the person surveyed was a child =

(Total no. of children who preferred Bubble gum ice cream)/(Total No. of children) = 25/117 = 0.214

5) The probability that the person surveyed was a adult given that they liked vanilla ice-cream =

   (Total no. of adults who preferred vanilla ice cream)/(Total No. of persons who liked vanilla ice-cream) = 24/46 = 0.5217