Harley's Daycare will run a promotional raffle that offers achance to win either a lifetime discount on merchandises (whichresults in a $1,000 savings) or a 5-year limited discount on anyparty-goods (which results in a $100 savings).

• Winning a lifetime discount has a 1-in-500 chance.

• Winning a 5-year limited discount has a 1-in-50 chance.

Is this promotion worth it if the tickets cost$15?

The promotion is not worth it.

ONLY if you cannot answer F1, forpartial credit (6 points) answer F2.

[F1 (13 points)] Some additional collected datais presented in the table below:

                       Enrollment Camp/DayCare	Infants (I)	Toddler (2-3Y) (T)	PreK_K (K)
ParentsOasis (PO)	0	10	50	60
SunAndFun (SF)	8	32	20	60
NoPlaceLikeHome (NH)	10	20	40	70
	18	62	110	190

Give the literal formula first (not with numbers) and thensolve: “what is the probability of not being aToddler?”	P(not toddler) = P(infants) + P(pre k)                          = 9.47   + 57.89                          = .6736----->67.4%
Give the literal formula first (not with numbers) and thensolve: “What is the probability of being an infant or toddlergiven that you are attending the NoPlaceLikeHomecamp?”
Give the literal formula first (not with numbers) and thensolve: “what is the probability of being a Pre-K_K child attendingParentsOasis camp?”
Give the literal formula first (not with numbers) and thensolve: “What is the probability of being in the Toddler or PreK_K groupand attending SunAndFun.”
Is there any relationship between being a toddler and attendinga specific Camp/Daycare? Explain based on “given” probabilitiesvalues.

F2. Partial Credit. Answer to it ONLY if you cannotanswer F1

Another survey examines the parent’s preference in having lunchprovided by the SummerIsFun Co. or lunch brought from home, basedon their children’s age. Some parents might not care, anypossibility is OK.

	Camp/Daycare Food (D)	Home Food (H)
Parent (Infant/Toddler) IT	50	100	150
Parent (pre-K,K) PK	85	65	150
	135	165	300

a) Compute the Marginal Probabilities and the JointProbabilities.

Joint probabilities:	Marginal probabilities:
P(D&IT) = 16.66%	P(D) = 45%
P(D&PK = 28.33%	P(H) = 55%
P(H&IT) = 33.33%	P(IT) =50%
P(H&PK) = 21.66%	P(PK) = 50%

b) Compute: P(IT|H), P(IT or D)   

[G(28 points)]

Overall, the amount of days attended (per summer) is normallydistributed around 35 days with a standard deviation of 4 days.

What’s the probability that the number of attended dayswill be above 28?
What percentile does an attendance of 35 days rankat?
What is the probability of attending between 33 and 39days?
The parents with children at or below the 10%ile ofnumber of days attended need to bring an explanatorynote.   What will be the threshold of 10%?
How likely (what is the probability) is it to have thenumber of days attended less than 30?
Children that are in the top 15% of attendance willreceive a ticket to see the DubbleCamp.   What is theminimum number of days of attendance in order to receive such aticket?
If 49 children (49 = size of the sample) selectedrandomly attend the summer camp, what’s the likelihood that theirmean number of attended days will be within 2 days of thepopulation mean?