Answer:
P(w = $1) = 1/10
P(w = $10) = 5/10
P(w = $25) = 4/10
Step-by-step explanation:
Let S1, S2, S3, S4 and S5 be the slips of paper, where we make the next identifications
S1: $1, S2: $1, S3: $10, S4: $10 and S5: $25. The number of different subsets of size 2 that we can get with the five slips of paper is given by 5C2 = 10 (combinations). Let's define the following events
A: the winner of the contest gets $1
B: the winner of the contest gets $10
C: the winner of the contest gets $25
So,
A={(S1, S2)}
B={(S1, S3), (S2, S3), (S1, S4), (S2, S4), (S3, S4)}
C={(S1, S5), (S2, S5), (S3, S5), (S4, S5)}
The random variable w can only take the values $1, $10 or $25. Then
P(w = $1) = P(A) = 1/10
P(w = $10) = P(B) = 5/10
P(w = $25) = P(C) = 4/10
