Question

Age Category AMUSEMENT (Ride)	{0 -5}	{6 –17}	{18-35}	Over 35
Bouncing Houses (BH)	140	100	30	5	275
Horror Tunnels (HT)	30	100	75	40	245
Ruffle (R)	0	60	80	100	240
	170	260	185	145	760

1. Give the literal formula first (not with numbers) and then solve: “What is the probability of being in the youngest age category given that you prefer Bouncing Houses”
2. Give the literal formula first (not with numbers) and then solve: “What is the probability of being in the {18-35} age group and participate in ruffles.”
3. Give the literal formula first (not with numbers) and then solve: “What is the probability of being in the {0-5} or {6-17} category given that you attend the Horror Tunnels rides”.
Give the literal formula first (not with numbers) and then solve: “What is the probability of not attending a Bouncing Houses amusement”
Is there any relationship between being a member older than 35 and attending a specific amusement type (relationship between age and amusement type); explain it based on the probability values

Answer 1

(1) Prob. = No. of people belonging to age group {0, 5} and prefering Bouncing Houses/No. of people prefering Boucing Houses = 140/275 = 0.5091

(2) Prob. = No. of people being in the {18-35} age group and participating in ruffles/Total no. of people = 80/760 = 0.1053

(3) Prob. = No. of people being in the {0-5} or {6-17} category and attending the Horror Tunnels rides/No. of people attending the Horror Tunnels rides = 130/245 = 0.5306

(4) Prob. = No. of people attending Horror Tunnels ride or Ruffles/Total no. of people = 485/760 = 0.6382

(5) Prob.(being in the age group over 35 and prefering Boucing Houses) Prob.(being in the Over 35 category) * Prob.(prefering Boucing Houses)
=> (5/760) (145/760) * (275/760)
Hence, we can say that there is indeed a relationship between being a member older than 35 and attending a specific amusement type (in this case, Bouncing Houses). This is applicable for all the 3 amusement types.