1.
Probability of the prize P5,000.00:
p1=10001⋅53=50003
Probability of the prize P10,000.00:
p2=10001⋅51=50001
Probability of the prize P20,000.00:
p3=10001⋅51=50001
The expected value of a ticket:
E(X)=100⋅0.999+(100−5000)⋅3/5000+(100−10000)⋅1/5000
+(100−20000)⋅1/5000=99.9−500044500=99.9−8.9=P 91
2.
Let's say I get X as a bonus.
Then X=0, 100, 500, 1000
There are 52 cards.
P(X=500)=12/52
P(X=1000)= 4/52
P(X=100)=26/52-2/52-6/52 = 18/52 [Exclude events that exists in other possibilities]
P(X=0)=1-12/52-4/52-18/52=18/52
So, the expected value that you can possibly win
E= 0*18/52 + 100*18/52 + 500*12/52 + 1000*4/52=157.7
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