Question

Some additional collected data is presented in the table below:

Age Category AMUSEMENT	PK	K	Elementary school	Middle school
Eggs Coloring (EC)	40	30	10	15
Bunnies Hoping (BH)	30	100	20	40
Roller Coaster (RC)	5	60	80	30

Give the literal formula first (not with numbers) and then solve: “What is the probability of being in PK category given that you will ride a Roller Coasters”
Give the literal formula first (not with numbers) and then solve: “What is the probability of being in the Elementary or Middle school and participate in Bunnies Hoping.”
Give the literal formula first (not with numbers) and then solve: “What is the probability of being in PK or K given that you prefer Roller Coaster
Give the literal formula first (not with numbers) and then solve: “What is the probability of not attending a Bunnies Hoping amusement”
Is there any relationship between being a participant attending the middle school and the amusement type; explain it based on the probability values.

Answer 1

From the given data, the following Table is calculated:

	PK	K	Elementary school	Middle school	Total
EC	40	30	10	15	95
BH	30	100	20	40	190
RC	5	60	80	30	175
Total	75	190	110	85	460

(a)

(i) Literal Formula:

P(PK/RC)

(ii) Solution:
P(PK/RC) = P(PK AND RC)/ P(RC) = 5/175 = 0.0286

(b)

(i) Literal Formula:

P(Elementary or Middle school AND BH)

(ii) Solution:

P(Elementary or Middle school AND BH) = 60/460 = 0.1304

(c)

(i) Literal Formula:

P(PK or K/RC)

(ii) Solution:

P(PK or K/RC) = P(PK or K AND RC)/P(RC) = 65/175 = 0.3714

(d)

(i) Literal Formula:

P(Not BH)

(ii) Solution:

P(Not BH) = 1 - P(BH) = 1 - 190/460 = 1- 0.4130 = 0.5870

(e)

P(Middle school) = 85/460 = 0.1848

P(EC) = 95/460 =0.2065

So,

P(Middle school) X P(EC) = 0.1848 X 0.2065 = 0.0382

P(Middle school AND EC) = 15/460 = 0.0326

Since

P(Middle school) X P(EC) = 0.0382 P(Middle school AND EC) = 0.0326, we conclude that there is relationship between being a participant attending the middle school and the amusement type.