SOLUTION: Please help. Write each event in set notation and give the probability of the event. (1, 2, 3, 4, and 5) a.) both slips are marked with even numbers. b.) both slips are mark

Question 252430: Please help.
Write each event in set notation and give the probability of the event. (1, 2, 3, 4, and 5)
a.) both slips are marked with even numbers.
b.) both slips are marked with odd numbers.
c.) both slips are marked with the same number.
d.) one slip is marked with odd number, the other with an even number.

Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Let N = {1, 2, 3, 4, 5}
(a) without replacement - P(even and even) = 2/5 * 1/4 = 2/20 = 1/10.
A = {(2,4), (4,2)}
(a) with replacement - P(even and even) = 2/5 * 2/5 = 4/25
A = {(2,2), (2,4), (4,2), (4,4)}
(b) without replacement P(odd and odd) = 3/5 * 2/4 = 6/20 = 3/10
B = {(1,3), (1,5), (3,1), (3,5), (5,1), (5,3)}
(b) with replacement P(odd and odd) = 3/5 * 3/5 = 9/25
B = {(1,1), (1,3), (1,5), (3,1), (3,3) (3,5), (5,1), (5,3), (5,5)}
(c) with replacement only: P (X and X) = 1/5 * 1/5 = 1/25
C = {(1,1), (2,2), (3,3), (4,4), (5,5)} - -> only one choice can be used.
(d) without replacement - P(odd and even). This means P(odd and even) OR P(even and odd). So, we have 2 x P(even and odd).
without replacement - 2 x P(even and odd) = 2 * 2/5 * 3/4 = 12/20 = 3/5
D = {(2,1), (2,3), (2,5), (4,1), (4,3), (4,5), (1,2), (1,4), (3,2), (3,4), (5,2), (5,4)}
with replacement - 2 x P(even and odd) = 2 * 2/5 * 3/5 = 12/25.
D = {(2,1), (2,3), (2,5), (4,1), (4,3), (4,5), (1,2), (1,4), (3,2), (3,4), (5,2), (5,4)}
Hope that helps.

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